Class 12th Mathematics Part Ii CBSE Solution
Exercise 12.1- Maximise Z = 3x + 4y subject to the constraints : x + y ≤ 4, x ≥ 0, y ≥ 0.…
- Minimise Z = - 3x + 4 y subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.…
- Maximise Z = 5x + 3y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0.…
- Minimize Z = 3x + 5y such that x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0.
- Maximize Z = 3x + 2y subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.…
- Minimize Z = x + 2y subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0. Show that the…
- Minimize and Maximize Z = 5x + 10 y subject to x + 2y ≤ 120, x + y ≥ 60, x - 2y…
- Minimize and Maximize Z = x + 2y subject to x + 2y ≥ 100, 2x - y ≤ 0, 2x + y ≤…
- Maximize Z = - x + 2y, subject to the constraints: x ≥ 3, x + y ≥ 5, x + 2y ≥…
- Maximize Z = x + y, subject to x - y ≤ -1, -x + y ≤ 0, x, y ≥ 0.
Exercise 12.2- Reshma wishes to mix two types of food P and Q in such a way that the vitamin…
- One kind of cake requires 200g of flour and 25g of fat, and another kind of…
- A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5…
- A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A…
- A factory manufactures two types of screws, A and B. Each type of screw…
- A cottage industry manufactures pedestal lamps and wooden shades, each…
- A company manufactures two types of novelty souvenirs made of plywood.…
- A merchant plans to sell two types of personal computers - a desktop model and…
- A diet is to contain at least 80 units of vitamin A and 100 units of minerals.…
- There are two types of fertilisers F1 and F2. F1 consists of 10% nitrogen and…
- The corner points of the feasible region determined by the following system of…
Miscellaneous Exercise- Refer to Example 9. How many packets of each food should be used to maximize…
- A farmer mixes two brands P and Q of cattle feed. Brand P, costing Rs 250 per…
- A dietician wishes to mix together two kinds of food X and Y in such a way that…
- A manufacturer makes two types of toys A and B. Three machines are needed for…
- An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made…
- Two godowns A and B have grain capacity of 100 quintals and 50 quintals…
- An oil company has two depots A and B with capacities of 7000 L and 4000 L…
- A fruit grower can use two types of fertilizer in his garden, brand P and brand…
- Refer to Question 8. If the grower wants to maximise the amount of nitrogen…
- A toy company manufactures two types of dolls, A and B. Market tests and…
- Maximise Z = 3x + 4y subject to the constraints : x + y ≤ 4, x ≥ 0, y ≥ 0.…
- Minimise Z = - 3x + 4 y subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.…
- Maximise Z = 5x + 3y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0.…
- Minimize Z = 3x + 5y such that x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0.
- Maximize Z = 3x + 2y subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.…
- Minimize Z = x + 2y subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0. Show that the…
- Minimize and Maximize Z = 5x + 10 y subject to x + 2y ≤ 120, x + y ≥ 60, x - 2y…
- Minimize and Maximize Z = x + 2y subject to x + 2y ≥ 100, 2x - y ≤ 0, 2x + y ≤…
- Maximize Z = - x + 2y, subject to the constraints: x ≥ 3, x + y ≥ 5, x + 2y ≥…
- Maximize Z = x + y, subject to x - y ≤ -1, -x + y ≤ 0, x, y ≥ 0.
- Reshma wishes to mix two types of food P and Q in such a way that the vitamin…
- One kind of cake requires 200g of flour and 25g of fat, and another kind of…
- A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5…
- A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A…
- A factory manufactures two types of screws, A and B. Each type of screw…
- A cottage industry manufactures pedestal lamps and wooden shades, each…
- A company manufactures two types of novelty souvenirs made of plywood.…
- A merchant plans to sell two types of personal computers - a desktop model and…
- A diet is to contain at least 80 units of vitamin A and 100 units of minerals.…
- There are two types of fertilisers F1 and F2. F1 consists of 10% nitrogen and…
- The corner points of the feasible region determined by the following system of…
- Refer to Example 9. How many packets of each food should be used to maximize…
- A farmer mixes two brands P and Q of cattle feed. Brand P, costing Rs 250 per…
- A dietician wishes to mix together two kinds of food X and Y in such a way that…
- A manufacturer makes two types of toys A and B. Three machines are needed for…
- An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made…
- Two godowns A and B have grain capacity of 100 quintals and 50 quintals…
- An oil company has two depots A and B with capacities of 7000 L and 4000 L…
- A fruit grower can use two types of fertilizer in his garden, brand P and brand…
- Refer to Question 8. If the grower wants to maximise the amount of nitrogen…
- A toy company manufactures two types of dolls, A and B. Market tests and…
Exercise 12.1
Question 1.Maximise Z = 3x + 4y subject to the constraints : x + y ≤ 4, x ≥ 0, y ≥ 0.
Answer:It is given in the question that,
Z = 3x + 4y
We have to subject on the following equation:
x ≥ 0, y ≥ 0, x + y ≤ 4
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGgAAABZCAIAAABdWPb+AAAAAXNSR0IArs4c6QAABHFJREFUeF7tnTtOJDEQhnf2BggiQuAInIAERIwEIiDnACTcACQyEA+JlMcBkEBIJBASQEQChEQ8jsD+q5K8poftLv9j98DwO2g10y5X+XPZrplxDZ339/dfKukEfqeLSOIvAYEj/UDgSHCdsMZ1Oh2yjR8jFu8HH8AV3SgwMIPUvqYqOV8ETuBIAqSYPE7gSAKk2BfyuPX19YmJCWy+KAsLC7e3t2SfmsSOjo6gYmZmpqli7XOECFZQK9yXuKlvf3l5uWLm0NDQw8OD3xKn/YeHh6Zoenra33g3n3+wnIqTlMWVa9q/ubnBU5C6vLyEyPPzs3HE1a/OY78pWl1dbQMcuoEuoeAmdAMW4JWkQavp2NraGp7CF2JMpjQjOLPZBqMNcFADR4g1geDk5OT4+HiMsrGHNeAwAHhamZifvlijpd7j0Diozc/Ph3UpadT5qWpOgSuasHmEAWyE5ZyqxqjSmmm0yespNeBspFHCSLfkcWa3dc8WiMq06rFjRcF1U2tvqhoXW+xS1+zAtHGqFvI4W2f+V2wOeUrFfiaOe319rTGFfvTy8hLLXlxc4M/R0VG6wbKCHo8IUxUeZ1PVP1Ce9tvZVSsLbqubw8nJSVjs/Mt22Mj+NyNai+PiUWwDHHjZthAvdpXIrnGZqA8XWnvnEEaxODiLgLCXx2gqkV0jNdvI6qthwiI2tIUJAVfGcKdbb+/hiD46924hlY/+mV3Vq2qg6wkcObwCJ3AkAVJMHidwJAFSTB4ncCQBUkweJ3AkAVJMHidwJAFSTB4ncCQBUkweJ3AkAVJMHidwJAFSTB5HglOeQwI4+8rJir6s8YLTlzVeUvX1tMaRHAVO4EgCpJg8boDA5clD6AKSOY/Cc37Nc6amsQ460lgHFXLlIVR0ZT8N9SXyHEInM+YhxOBKnL9rBmcnurpzNXC+DKeyPE7UeLDQKuTNQ4gNK3HisxkcLACg7gQR0Ew60Fo/VbPnIcTgSuRRuHbVlZWVt7e38/PzsODu7u7ifm5ujtyTPorh2DROEmJ4tra2sjT4aSNjY2Px61NTU/jz6emJ0+gCZ4A2NjZMB/q5vb2NrlZM4SxAa5bId3p6Ojw8zDXSvpQLHPqDNe76+vrq6gom7u/v47q0tJTF3Lu7O7SMMjIyYjmX9nsUZ2dnuEEMkUVL9kZc4KB1cXER14ODA1z39vYwrWZnZ7NbU7TBzHkU/jjOTjZbnLWzs+PfT527atwgVPR4KvxL7KpmBGChP5aVlJQ32Hdw/YnjwtABlk2lpPxbv0eX8zi03Od3DqY+Naem7x5nBuTNo0j76Bw/NgBw9/f3xCr+c38iCLEI4nsEwwS1wRPxhiPo+ebmJnaGXO8WvjtKL7jHx8fj42P8HMg3Cu6Ljk3aGteLKT93jeuF2uDJeqfq4PW8xx4JHAlQ4ASOJECKyeMEjiRAisnjBI4kQIrJ4wSOJECKyeMEjiRAisnjBI4kQIopzyEBHL7xCbXL/o+FBKO+W1WtceSICZzAkQRIsT+8CbtfHqivlgAAAABJRU5ErkJggg==)
(x, y) = (0, 4), (4, 0)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
We can clearly see that Z is maximum at (0, 4). Hence, maximum value of Z will be 16
Question 2.Minimise Z = – 3x + 4 y subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.
Answer:It is given in the question that,
Z = - 3x + 4y
We have to subject on the following equation:
x +2y ≤ 8, 3x+2y ≤ 12, x ≥ 0, y ≤ 0
3x+2y ≤ 12
![](data:image/png;base64,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)
(x, y) = (0, 6), (4, 0)
x+2y ≤ 8
![](data:image/png;base64,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)
(x, y) = (0, 4), (8, 0)
![](data:image/png;base64,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)
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)
We can clearly see that Z is minimum at (4, 0). Hence, minimum value of Z will be - 12
Question 3.Maximise Z = 5x + 3y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0.
Answer:It is given in the question that,
Z = 5x + 3y
We have to subject on the following equation:
3x +5y ≤ 15, 5x+2y ≤ 10, x ≥ 0, y ≤ 0
5x+2y ≤ 10
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHcAAABZCAIAAACL/SybAAAAAXNSR0IArs4c6QAABNBJREFUeF7tnM8uJUEUxufOA0iwszT2Np7AhlhL8AhsJQhegKWFeAM8AJFIWLASCx6ApRXxCOabOUnpqdtdXV1V58zNvV8vpPWf89X51ek61ek6t/f19fWDmzKBn8r2af4PAVK2iANStqDcc+Nyr9ezEBwljW+2VcqWmRCdOsRyiKWqgxwxLB4uUiZlCwIWGoxlUrYgYKHRHssfHx8zMzPImK+vr16L9vb2cPzy8lKjpYeHh6KLbXV19fn5WUNFbMLHs7OzxcVFkZuYmCisiOmUbBBz+97O3d0dzi4sLFSPy8GVlZWmu8LHA3K4cX193WM6Pj7+8vKSphX2DmfFFz3Fb7Jht3d3d3HBycmJ+Pn+/v7r74adNM8Dck9PTzgLrHBetAQ6/qZpxVCG8YuLC3EH3Tk3NwdFeF1EMZYy5CHsAkqgC4W0LUD54OAAZ09PT6uWIY0tTauVcr/Z2se3k3rVwVjKEJAQw7ghLcjp57DbkIB9b3yoPRjvdvhJbaKM/o6X8K5MpAwrEmWIKcR1srzcGHBbgHr2RTr56elKGfmmv6c7uVxVbJ9jVHPC1tYW/v38/Nzc3OxPF0NzBPON8/NzDFnT09NFnOpGGVM3ieX9/X3Mfoq0YNCMwMe1tTUgxmSuWNvcU9D6TLnhGLk4M+PHjBje7MVgXHaTGS/xdhooannGZj9v6ibDFnCntSBM+b/MMZDbZRKFnWSnqjemZD+ZsbrkA+gytRqO+TLCRVJ6sjv9HdOZsgwR3tRNDg7Hu588PbVbkVlN+4ghYVs7dcsZN1rTADzHu6V4DqHMBzksp035n+9+MlzabPwiZcN5hFS6zZdHCExRV0m5KM4GY6RMyhYELDQYy6RsQcBCg7FMyhYELDQYy6RsQcBCg7FMyhYELDQYy6RsQcBCg7FMyhYELDQYy6RsQcBCg/V+ipTdd1R+XdWizHo/LbJNdpn9LIiTMilbELDQYCwPBuWNjY3aoj6sEkddHEryNJrpSu+kAM9tGlrOpmKFYesq8aZFtN5a265rfuFb4BZZE96/dVVp9c5doFph2L7mE+3A2nQ4XF1Zm18mFUM5mWl4NXH/We0KwyjKaJYElytzzCypDK/Fd3JmlLVX/8dSRvUdKMsqZmlTTrnDoFHWrjCMnWOgJgtwHx8fUUK0vb2NZdtLS0uquQjGXdJDuZJSTX3VBa/ubH5+Hmff3t4KuBmfH3ClLI7PKSeJlKvNfjmlSwlpoGAdZ2wsS38eHR3h787OzuTkZIEebjZxdXXl+gODlTiMOaWqqJ7xbpTHxsb0mtJkGQ8yamYR3aiZVVX36kRvbm4gNzU1lS/ajXK+XrIF1VJZGYKvr6+rzXt4eMDYWKRIeBAp4x0Mg4NLd/iNGfyLxNv0qpLcc+5GsQyV+/t77KBHsY9Hp1iRcGQ6ksvkZSTn9wxi5GrrwjKrSsPZD61SffcbxFheXl7Gj8q4yAVfIEAsz87O5odtk4Xj42OvwvD29rbIcAFFfpHS6jh+kdIi22R3EEcMawb6eqSsz5i/JW7BmJRJ2YaAhQrHZVK2IGChwVgmZQsCFhqMZVK2IGChwVgmZQsCFhqMZVK2IGChwVgmZQsCFhqMZQvKrPdTpFxT76eoNvKmOWJYhAApk7IFAQuN34b8HZUSm8g5AAAAAElFTkSuQmCC)
(x, y) = (0, 5), (2, 0)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(x, y) = (0, 3), (5, 0)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
We can clearly see that Z is maximum at
. Hence, maximum value of Z will be ![](data:image/png;base64,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)
Question 4.Minimize Z = 3x + 5y such that x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0.
Answer:It is given in the question that,
Z = 3x + 5y
We have to subject on the following equation:
x +3y ≥ 3, x+2y ≥ 2, x ≥ 0, y ≤ 0
x+y ≥ 2
![](data:image/png;base64,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)
(x, y) = (0, 2), (2, 0)
x+3y ≥ 3
![](data:image/png;base64,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)
(x, y) = (0, 1), (3, 0)
![](data:image/png;base64,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)
We can clearly see that the feasible region is unbounded and the corner points of the feasible region are ![](data:image/png;base64,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)
![](data:image/png;base64,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)
As per the table minimum value of Z is 7 but we can see that the feasible region is unbounded. Thus, 7 may or may not be the minimum value of Z
∴ We will plot the graph of inequality, ![](data:image/png;base64,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)
Here we will see is the resulting half plane has common points with the feasible region or not. As per the graph we can observe that the feasible region has no points in common with 3x + 5y < 7.
Hence, the minimum value of 7 is at![](data:image/png;base64,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)
Question 5.Maximize Z = 3x + 2y subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.
Answer:It is given in the question that,
Z = 3x + 2y
We have to subject on the following equation:
x +2y ≤ 10, 3x+y ≤ 15, x, y ≥ 0
3x+y ≤ 15
![](data:image/png;base64,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)
(x, y) = (0, 15), (5, 0)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(x, y) = (0, 5), (10, 0)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ4AAADtCAAAAABrWJPIAAAAAXNSR0IArs4c6QAABx5JREFUeNrtnV2B4yAUhY8FNGABD0iIhliIAxzEQRREAQZiIA7wcPYByE9TWtJkdmd2bl+2O23p13DvBc6hFPzWNwjeRTx8z9uC9y07Q/AE7zfhebgreKG3AGw/X8TrMKZ7Wt+HN+lt0bmAN6GNd0Z0t+EFDTOS9J2+2rlaBZJki/k2vB528/hoEGkJO7eA93CjgWoDSfoGMEN8R2/z5d40NZAklSHZaEA1U8Zz8LHVXTvv8ez2ow6xlweS0AqA91AAgG59tCc9zBoNS1MzmtjIsIyaan6Ct7bzHg+bPp2hRnJQKpBA+uhwM71SZFBqJCej8l8PmWsRSDYI+Q8ufpY93qadCrxN36be6TCSMNvAaUAOMTNHePpt8GNz8XsyxGsYhsYCcEe8TTvnrl5qw8Mt2AnPgXQ5w/0+2le8oEx+9znVgyd4m3bOxV4lnivhscXM2GktmnGKzyviuZOZu+vcA16/lN0i3ohujtXPYnneI96mnRN1r9cpNXqo8Axvhh4Dw9gWO5fU2mGKeJ4cmwVvRBM4WthdOzWjhlpHjW1hOeDlR/ECr4PS6ToCgFrwgor/t7t2qsZcF8fc8FCWD3j0jQKaody5nJaIGjS0Gxc8ThaqnXNZTu3IhErwBE/wBE/wBO8/xwsNoG/A8wAA+zBDtI+znd1yswLPbtb1i7hoP8XDfmF/GW9GE9YnXMJzZBgUXkssJ/H8ccIejJo+xCM7eHJqAO2WpYJFaBXMuFziuL7X7VzAC62KgoI7zoaDwcCP8Vr4PK1vVzyVVvoZzz9bYmFDAAAmPMNrK+hKeLODIjX6QG/gFzwzMrTol85t4MnJ9c/xWrQz53X5s6frLmQuMGQBbES34MXlg1vw2qIwQpJxFRRgjnhDFtc+wlONX5uE3eFxgzcpKOumAl5KH4sD3pAkkY9jj1V4DH2j8RBF7/EmZcJlvELn7vBIclb2XOdOSs28jJdSQ21SY4OnZ5JtP5GTtq9SwzymRk3Bq8E7FpYVLw5SdlURXhaWHZ67PGpkvseyvOJNDWDoW30cn5+U5fvwZL4neIIneIIneIIneIIneIIneL8ITzZnSuwJ3g/Hc3XSJTnE7VF/F2+Kb+pKu0tWYYj9S/GWJDtkZam0Eeksno2bFkt4k9rYMum5JbwwqLvxstblnuzKIckGbaBPtowv7cvi8gn3rV7u3LwbsIQXnbvcrUb/ZTzV8BWej3mT/mHawVWMPXsz3pSj3QGA6Y94q15P0h/NnQIeAN2Fq3g+X7SUGu1rvHC8KmW8qDPfg5czb3qJx0o8Mu5n6+/EexKBaRdrjr1TeKcj8C1ed0iQfeaGU3jjZbycGt4OgSFuzGS3CcFd3atODd3P5KgKxep8YVmdSZJmE4G7UeN1YXHrSIHnifZxWQ5Do4DGM9tiz8bcmrIc8cZWF/bFfzio7UKm1O7rQe1LZizHYb5Tpde/mRJ84YRqczMlY/39hOrXTUdlrSF4gid4gid4gid4gvc/4omvIbEneD8c70f4GknuObxk7gyg48EE9b4Gx2Z51V0ixqSenDyRNgObGhFj9TWGm8TbjaoTtLFHvMZN5GQ232p/rVAlWQ4DOV0Xb9dTDoIxwZYCKYu6tb5G+hrzdVco+xo0OrCENyqTCep8Das8SYf5It7ia7RqYgEPUC7kUKgTb4OFdk4NV1MjS9+tmljGg0470Wul79CaVsP6u/Beb2zPqVFtHBhL0tvyCQm34q1BXoc3Rq7wfhd/Jd7+wz8ZMNyZznXxadfxpl1pSq1vfQ0zbB2KytSYoPrAqTnpHLwqLJvWt77G3qGo9TXaeFeH28ryirfzNfYORa2vwcHcYpiKr3HbhCr3oPgastYQPMETPMETPMETPMETvO+LJ7aLxJ7g/XC8n2G7rGeOPsgqq7BzwnbZbYi9QWNJRsn4Cq/edtlvJ75BoVLoyf54rtpOlKq2XfabsS/gJX0vbYpvDvLinqjadtFFyegcXlJHXdT03EHa2+NV2i4PX0L5HC9ry65kmu2/GFKpLT9+jeJjvKzMv8ZbvMVKZf7v4eWik6Lon+GNz2PvIQJr8bp7Ys8vhkUhc9PlO2e73Ja5i+2yrXtb22X/xZBaR/K2updtl+2ocd12uW3UWGyXdcy9w3a5a8wV2+WWCdVmYBXbRdYagid4gid4gid4gid4vxpPfA2JPcH74Xg/2tc4c0yW0+n3He8XMUq+xoljstrlpy3vw3vna9QfkzVBeYb27CEsVQJaUR2tPyYrCb9K3Yn3xtc4cUxW+klKi/k+vHe+xoljspbt/P4+vHfGwYljsr4BHv8Z3liIvepjsuLv094be299jfpjsr4ic9/6GvXHZH1J3Xvna5w4JusrRo13vsaJY7K+YswVX+OWCdV6E19D1hqCJ3iCJ3iCJ3iCJ3i/G+97+xrf+CZ4gvevbn8AcFU84IYMSaIAAAAASUVORK5CYII=)
We can clearly see that Z is maximum at (4, 3). Hence, maximum value of Z will be 18
Question 6.Minimize Z = x + 2y subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0. Show that the minimum of Z occurs at more than two points.
Answer:It is given in the question that,
Z = x + 2y
We have to subject on the following equation:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(x, y) = (0, 3), (6, 0)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(x, y) = (0, 3), (1, 1)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARYAAADxCAMAAAA5pWjzAAAAAXNSR0ICQMB9xQAAAc5QTFRFgYGB////AAAAd3d3Znd3ZmZmZnd3f39dbn9/f3d3d3ddZnd3gHNmZnN/Zn9mf2ZmgHNVVXOAUW5/f2JVWWJ/dXVTV3NiZmJif2RESGR/fWRESGR9WVVzRmRkZFdTWVdkRldzdVVEc1czN1dzc1UzZEZEN1diSEZiZVYxV1YyN1ZUN0ZjZEYxRzRVWDRDRjRUZkcdZUcdI0diRzREVzQxNjRVV0YcSCFER0YdVzUdJDVVRyFDVzUdIzVUJDNDRyExNyFDNyExRyEdNyExJSFFRyEcJCFEOCEdNyEdJCExqqmoqamoqainJCEdwcC/wL++wcCnwcCOqcC/kcC/waiOwah1qainqKinqaemqKemqaiSkai/qah9qKd9qah1lainlaeneai/gKinkah1wZBagKh9qZRnqZBakZCOa5SngJRnqYBRXpC/gICSXpCOqXc9kXd1eXeOVYCnXnenlWo4Q3enQ3eOkVw9kVwda2o4XlyOPWqSgFM4gFMdVVN9XlwdeUFaeUE9JFyOXkF1eUEdaztRJFN9Q0F1azsdJEF1XiFaJDtnXiE9VSFRXiEdQyFaVSEdPSFRSyEdPSE4QyEdJCFaJCFRJCFHJCE4JCEdmTRy0AAAAE50Uk5TAAEBDQ4ODxsbGxwcKCk1NTY2N0NDRFBQUVFSUl1ra2trbHp6e4eHh4iVlZWWoqOjpaamsbKys8DBwcHBwsLQ0NDe39/f4ODu7+/+/v7+kyY+/AAADXxJREFUeNrtnf2fE0cZwIfdeLv01O7VWnfFtzaLVFTOXMWKJO31bMIdduNxyCiIoueJIqcoHnpK8eWKWKzSqwI6/62fmX2Z1yR7l90kmzzzA4Rhs9l888zzPPPMM88gBA1aOc1uko7rtDsuoFC4BAh9aQFAKM1v1ZzFGnDQxcUPAIPWwtdeAc2iN6e9BBAM7UVQuCZpAYVr1C2gcA1QCGgWaL0anpVmHQyL3kXyXZavy9CHUYE3M3Wdt/L1HQgLIQSwAJZ8WAgxcZl1LASw9MZCAIs+isASARbAAlgAC2ABLJOBpUGyOAtgye7aaNVQYwmwyHe1m3W2bgZYFCytGgrrIC3KXb3VpSzgD1j4XX2SJCkcYAZt5eky9OEjhquOoOIuO39keCysXfnbT/efbtJXMZZulVp5sdxGPbZGsbx0q9VKG0ROO0DIOesCFt0S+SAt6iCym4S0MksEWIxzIsACWAALYAEsgAWwABbAAlimAUtIowlrC4BFmUFTLDBVVLA8S0MKfh0GkUG3pJuIAIuIRQhxAxaOJRlDFYzlHiktxI0xfvsGhhC3Ji18XwgMIgFLaocAi4SFb2YFLByLsLcKsMCcCLAAFsACWAALYAEsVcQS8jQxwJJ5ubzAD2DJsIhVOAALz50TikEBFh75P9lOVQtgybD45LRrN0HlqlgoEZ8E1cRSWiz3Jk1Vvrp/G2K5el6u901YbFXXoDuusJ8IsBh3nwEWmBMBFsACWAALYAEsgAWwAJbpxeKtZt4/YOFYaL5yAFjUEPcJGEQGLH4mK4CFY6H7fSGwYLJEdhN0i9FAx9E5SFeW05XxzQeQrmyQFh8GkQGLdxq2QihYqI/bguR2mBMBFsACWAALYAEsgAWwTB0WHwqsGbA4bcBiwHL8C4BFx+IHIWAxRf4Bi47luAtYDPGW51GFsZQWy70XR3AhXdmwzQoGEWABLDAnGhYLP/gNsOhcAAtgQegAwwiwqN+esQEsOhbjubUzbqBJNpgAi8FvUcHMEhZ6bkrI8wZpJdiAdWJNYmYIC93o7HdctoM1hdRx6WZWnA2lYOawUAx2M8jC+0drCDmvLyDkLW8m/88lZnaw0FOZ2DbndK8zDT19kU0QH2SYUjAzg4UJBisYkI6iLCfM+8DlmGIwM4MlLqEgYQlJXIHD2Q9ETJTLzGAJMyzeapbDHpI6w1KXMKHKhSwPH8tlWFTdwk7eRM7+3STWuUPuzlheLhMUZomyEBzVw4E4iBJM6RRyZlQuNc5c46bKhKvcGFM8WaoWmKEMNEq8XG+14/rZYQexgVbSlSumYg7vzr2+IPzrYwuCn7eZbCcS05VRtXTv4Z1/QdWKtdScdtDn9PCqgBlyqmjs7HeoercaYEa1IMJfd6vAZfRYKgFmHFgqAGY8WCYezLiwTDiY8WFBuAeYre3ZxtJLYnbJnanAQviyPBLPPgsGYTH7d1sPN3b3pkFaJCrs+9qn6LJAMBCLCcyl9/+8HY+kW9tTgEWUFjpJsptLObAgFClcbpGExvpvGKXHDzcqqlukYZR930Y+LDKYLfK7+9vd7oVH5A4TGTqknlysqMolSUiFSDUWgpxYOJj1+w83urt3EqmhGubntPNOVS0RyYQm+75ZuCUHFg7mO9/fInuJpd4ibPxUHUsMxnSaVR47znXvLYbh1xsUEuUz8kFUfLoyA8MC3LeTSHCsdvLEjCWjdOm3qbZ5cnHUJqmMdOVYxdAD4WiGuyYt3moctcMmAYo0N+bCoz06jMh2JQeRlshBGy9oL6wZtGrxEQDYPK5kMLcIG0Dr97e7F/5IPeDtCmNJLbbJQH8iXSjBvdSNAGaXxOqXYlm/Twn9/seVnhNJfq+icgdgoVxIVyKzfn97/a8MSPJXdaeKREzk0Nfe+mDRHd/u7q/+meBY/8tFpnFImb5vqTNowhM5FCq0DBDO7fhSLNxGX/jHxQuPnlzsXvr7RjWxZGBELPHqSYPUcU7Hl6F4Z4PNjmKV9d9/71V3EJlmkdlJTn6rdo8p5DAY6PjuPvnJ+5I/t/vwZ2Sv2lhk5ZvV/veWv36bjiT7s30d3xjMD9+Rhsulx9vMNFU9OielXcZkQhJgp03qftA/rofMYaput9xA1aiClnKirk8+32RrsiFZGoBFdHyTv7f2qCW6Mw1YRImxm60aajCV6wc+adXCwOqDBalgqP7dKjc0NcIQtwDmwx/xyRK97DM1+o+s+GUOx5e+uPS4ZI1bIhYmE3oiB08zu4uQ97ksXuWcsFDjdm/G0UgXlUrD4rSJhkUGg4XJQIDYgWBvL/QRvVGCKXEQhQYsIhgJi/1VSuQK+1OocNLP8Z0qLByM8IUbn45zqzBdR0Heshtmpw/2dHynDUsKRsSSUMBWkkvEExV7RHynEUvsx/Av7CzOWaw2KAtdzVt0Njmf2mxrsH9XhVhuVkZ4571rvWO5vOfe0198sCn939Vfvvsgd8S3OrFcVVoIIcb9i0nfxxcV/Xr0a4Lvi00fUDqY8Qyi7MsRszX2+Xmv2PwBJeuYErE0BmHRN3tihJxPUaIDpKV0N6ZMd46sLeRK5LDELj+qW2IqNEZ9Qr5TmvajgmFdYSQcmdwPS4lgxo8lDvRb/aeKfUK+U4uFgzFhsfp/QDm6dzKwpGCw0V4N+IAywEwKlhiMLhoRGYilDDCTg0XUMUo+Ua6o6NRiYd/OGkzF8E5csMRMFhb27aQPIxjlw1KsUSocS9hxh8GCZDDkAFiKBFM0Fpp0OhwWEYyxolJvLMWBKR5LMDQWrnsJOiCWosAUjcVZrA2PJQVDDoGlGDAFYbGbZO2F9toCmwAn9VuGwRKDoSKTE4uFCgUzEEFkJX32GbL2wsraQi9V26odd/lTEzIIi0mZEt2NMb3T4MkQ1QWKF9rUZuoihi4di+I5UP33Vtz1UmvuuNtHXnhUWg3H5cZi6SFfy4DF0rFYhmjxt/UvbOjS+wwf8JaOJb3KPkOC3uOI74sms9MYGO+N5/ro2pfTMEkS1JaC0oZANc7VZ0h0znk3U4o0uWy47HKOLvWdAhXnyy935nuNoVNutiGkIN2SdqmObx7dklwWKe/E+TRVPt2STGztU/OosWT11CzeKhHTs4vCYiEVTJRDt6QqSL72svGyPMpLx2KlligKvHORUK1lmDmR3WxdU4dhO9J0V7q1TwZzU3uI6/zsaf4YcfRTAEOPYiayLW1ERPulG4TUlWetUQRhRI4VMlVMq/VpWGg+wzV9GO4oXJyzLk6WowUwzr6GZUcocpddleq6FIyzQniZkPiRGq0abig8G0vYWRG4OCuEYfHfdJ2VYwVgyar1GQQ1VLHQbXxXmvIjHq0hnC0DZGCO/0HF4vxJe0Kn/UAdds/SSaxfT2+WpJNjX76bt+xicaEq9snOW0mRvbmhsfBqfXmwsHeqvxxCOC5mJ4Dxgx0Vi09k8War/Zu6PsJ8k1PEsJxpzeGwLt+LhgCEOmApFrUQ1qGx8BvlxXKlqTlG10/XZAPwzAmkYrHPEFW1OO2T+0SymxGLFTvJym7yQN65pR8syjfz154zYlGK7B0eC79RXiwyAyRWaRMlRpMWhFVX0yenN1mClfRWbCVjKLN5fvRU8TmcldaPLF9SzOPGYkoSC2Wz4D1P1eac/pHy+GNDwVfUcERIMobSB7JPfXRf9cW8c0T5LRIs80iWomGwsBvlxBKaUgqTKm2CRSW62aG6VMci/bbJ6sqcJQpLo45wQ5e9D8mfOV7d4texlW7jE27W0PTNjjaDxPzs6VS3BFj+Euwyv850b/o8lBt+Rivm9L1QJhVbojNKkb2hLFHYwxI1NCw+UYU3tkSavqEqN7HWWXqipV4WdjYtza5hOoaEpSdqiS5/8hvKB9jvKk/RaM19y6LG2VkJivBb0mp9JneO/E/+KcOIaPbEj4QqbRKWxFrHcKg20C5r6H4vuhpbnShDap+J1Hd656K7ig6OyNoNC6GXFC98OC9XqdeRMzrXp0sM+ar1C3IHRVOkOT+zhHWisrAISSAHxSKEuMaMBRWPhd/4kFjIOLGgsrBE/bA4/3KlHCI6/8XOq/MSFmucWPKuJB8i7adnj//mJtXsmU2h09aV21mAMcpG9lix5BRyK0+XoU/rcc7OY8tpZ7EUu3nMQv57c5a3PK+4PHoisqGruHTlQYHbUtu9uywTOsuDvv6fG8kfOw++W9SHHAzLBDQWpHHaJ9tRMuPh8zNv2Z2whw07o3qiuLA8Oe2ms2iORZsojbvZzaWR/gAJm0Cetjrt+qRhCUaPJREOPm2dOCzOYg2NchDFqiSeRfNp66QMIrtJaKi747J0/hGqXBR25rNZdDb/nRiVy36prH6WcqwR9T4DcwHrYVpcWP4rEZ1Fe+eo7ITJ/DdcmpTRQwMM6QBSjjVKX2sRo0LEJW1SYfmJsc92M0hjZ+qxRtnromXbe4MXll8RCsuvTJB5Dl97xeXCLUZF+euihdt51c3ZOT4blB4EoB1rNMneZ/ntxQXR+zRimTjvc4Qei3as0QR7nyPQLYHofZp1y8xhEWrXaMcaTZ73ObYJv3SsEfU+2xPlfY6jqccaTaL3OTZxmWzvcxyt97FGaKZbz2ONoEGDNuvt/8RoRzXXcE8QAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
As per the table minimum value of Z is 6 but we can see that the feasible region is unbounded. Thus, 6 may or may not be the minimum value of Z
∴ We will plot the graph of inequality, ![](data:image/png;base64,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)
Here we will see that there is no common point with the feasible region.
Hence, Z will be minimum on all points joining line (0, 3), (6, 0). Therefore, Z will be minimum on x + 2y = 6
Question 7.Minimize and Maximize Z = 5x + 10 y subject to x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x, y ≥ 0.
Answer:It is given in the question that,
Minimize and Maximize, Z = 5x + 10y
We have to subject on the following equation:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(x, y) = (0, 60), (120, 0)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(x, y) = (0, 0), (20, 10)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHQAAABWCAIAAACRnCVNAAAAAXNSR0IArs4c6QAABT9JREFUeF7tnb8vJVEUx/ftHyBBpxCxegU6lYYotJRKlCSIHyUJpUT4AyT4A0hEoqESBYWSUkXEX2C/uye5e/fOvPvOzNwz+3b3O8WLmXfv95z7uWfuPS8zJxqfn59feNgQ+GojS9UfBAjXMA4a/rLQaDQMTf0H0sEaG8K1W4Ixc3bi2Ymr2RwcyFrksmB4QxEu4RoSMJRm5BKuIQFDaVXkvr29DQwMYDd8fn4OfFlfX8f18/PzJD6enJzMzMxAUI6HhwdfFqfuW/izu7tbxSi6y6BwQDawVUX5V1+kR+7AVf/U//v6+hrfjo+PZy9OT08366UUR7PX11foBEOCUadwf3/f2dkZNFhbW2tmOjIWdJmfnw+kIP709KQZiN7ibzTjDmEkaHB4eCjqwPHt54E/ND5pxKF2dnaWKyjoAUW+BXdh3YxIxBzmCd+iu0weBIU1PjUDMYELJ4aHh90MC2s/uOKeRUYLQPg2Pk/SwDeBafYnO7AeMbezs4Nvj4+P/S4YF44/BheGZc6xOMgqEbkrs14WHW12/QkiS3xoFm4Rc/A/G/K5FwuxzlpUbWhueRocHMS0X1xcTE1NIYq3traClavc6dXVFTp+fHyMjIzIDpO7X/X19fn6o6OjOM3usUof+vv7/ZZjY2M4fXl5UXbXNCsGF4rLy8v4fH9/X1pa0hjQt5mbm7u7u5P2WChWVlYmJib03duwZWG4yL0wDCxPGxsbSNESDgmLoNvKsK3BBG4RkwwpodNRqWJwb25utre3sdQeHR0huDY3NxP6iWSzu7tbBCcnJ1dXV/EH+DoTWDd8c3AGp8HdrfcniAxZmnp6evQKLVsWgAtvZmdnsWUvLi5i8MiNDg4Okvx8GBoagqMCKzh6e3txRZbX09NT/9vHx0ecYhtoOciggSyvl5eX/vXb21vcK6WnKt8HfZ4vyaDLvXALS/pSPc91iSdWA/FHlgWYc2nsv5znYrQYapB7ycUkv9Akaw4OPxX9Z3+hSZAi98rmfRJQLuIiiSGaxdNGoIQJ4QvZ7M8T8HU/kbE6ISmsYg7dIeLMQbxQVqtJ5PmYp+iK3bQ9H/MkQ6kRKpAtaOTYxidAuIbxQLiEa0jAUJqRS7iGBAylGbmEa0jAUJqRS7iGBAylGbmEa0jAUJqRS7iGBAylGbmEa0jAUJqRS7iGBAylWYeWEi6eWvpyfECZDC4fUCZDqRHihqahVLIN4ZYEp+lGuBpKJdsQbklwmm4quAsLC7nFZniptKurC6/Yayy1bFNHYdjvTpiXvWleIW32tmjwUmnpah50TF4YBowRf5KXvUmGG1YUaeCiDV5BRGf/FdKiBT2R0VoUhsXhyhurCcveKsFFZykmcoVxhSr8cm27ebUoDIvAtSh7qwpXfJK3dAWH5rVcRzAyWovCsIi53LmsWPaWC1e1ock2gHoBuIVqJhT0oI4J7yGjMqLlNqVvUENhmDhTW9lbAbhwC0VoWA1Q0IMXzff39/Xg2rBlDWVvxeCC0d7eHj5Rx+TKmtoQnMalGsreCsPt6OjQuF6iTQ2FYb5XNZS9FYZbglrLLvUVhv10pb6yN2We65pJehuvpMnN3iPbd815rkXZW9VUTJBZwK3/F1rysre2hiu5c8LCsMiNIlGStuwtFy4f87TcEbQN+JhHSypJu7bIFpKMpA1FCNdwUgiXcA0JGEozcgnXkIChNCOXcA0JGEozcgnXkIChNCOXcA0JGEozcgnXkIChNCOXcA0JGEozcgnXkIChNOvQUsKVx5TuqPV/lKUcx9+gxTXXcJa+A/8c1shp8dTnAAAAAElFTkSuQmCC)
(x, y) = (60, 0), (0, 60)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ It is clear that at (60, 0) Z has its minimum value i.e. 300
Also, Z is minimum at two pints (60, 30) and (120, 0)
Hence, the value of Z will be maximum at all points joining (60, 30) and (120, 0)
Question 8.Minimize and Maximize Z = x + 2y subject to x + 2y ≥ 100, 2x – y ≤ 0, 2x + y ≤ 200; x, y ≥ 0.
Answer:It is given in the question that,
Minimize and Maximize, Z = x + 2y
We have to subject on the following equation:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(x, y) = (100, 0), (0, 200)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(x, y) = (0, 50), (100, 0)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(x, y) = (0, 0), (50, 100)
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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANcAAACZCAIAAAAzTTj+AAAAAXNSR0IArs4c6QAAFJFJREFUeF7tXcurXbUX/vU3L6J1JCKinYhCRW0FsYKCWh8TsT4KIoKibQcOrXrtSLxQUTqprQUFB4IW7sBBfRbqQHFQHygoDrRFRDpSi/UP0E8+SZdJdrJ2dvY+OeesPbjcc052svLly8prrax1f/311//sMQRmisD/Z1q6FW4I/IOAsdB4MHsE1rkRed26dbMXxyRYJgTOcU+y0OaIBRxA7zXcBuJmI3IBgPZKZQSMhZUBtewKEDAWFoBmr1RGwFhYGVDLrgABY2EBaJO+8umnn2IB9OKLL05aaqywt99+e+PGjRAGD/6vKE8PFv7222+HDx/etm0b5cCD//HNqVOnKgq0MFmtrKwAovfeey9aIzQnnjmqLDrDjh07Tp48SZl//vnnmsJjl4EPMnX/h/98/fXXl19+eVfBiRcX/qcu3IAYftq1a1eIwLvvvoufnn32WQ04n3zyCRLv27dPk3i8NKgIxIAwtYqQuKl0IbTgvffei35w3XXXAUEnB2QClAl21uwu85bXpk2bgAxGLqDnyX706FF88+ijj85RnTDiofVvvPHGUWTW6MJXX30VZd9+++3ZfgCOQlYK6lGW6haZgM3sWOxbrq+7d88//3wk+PXXX2VxSPbAAw+4nN966y3ZGagtkAb5M01W1FoJEmURNykqC0UFAY4TAPVyPRk/4SP0aFg7foNqhjopbJ0EXF0VT7SdxzwNE7LwStzOtVYCTTYt2JPOGnCHHUW2AX4F3ADaJXMslF/yVzlgRXNGG1Me8tixvx0WchYFVkncWBcPFg83oOHQ9kZkDQvTcEUbMd12TbCQ7ElTkIgDPjdko2L4iMdpNVYm2tepzAg9cOeLLBGv86PLGaoCnHMJ2E4yh2xHrJgg0XtRCjuw1OvU6J6ml/KQZ14fc/PCLAuzcIV117QdKzISbipdiOKzSjg6+kCf4V3HHmosrybR2TebiinZTeV8FF9ygs/JMnNQTvYr4sis0m1D4R2lQJFQO+JLJEOV3XSCPUpqej0Ls3CFCGjablQWqlYnAOXHH3/01LL38Y8//sA3F198sfz+jjvuwMdvv/3Wfblhw4Z0Pvz1mmuuccm4KXDXXXe5HSL8g49ePuedd54m54nT3HrrrdDZr732Gss9duwY/j788MNODMz6r7/+emyCHDly5MMPPxwunhIuWZCy7YbL1pWDioVcUjS4L/jZZ5+NB02VnNHrHnzwwS+++ILovfzyyyDlnXfe6TJ/6aWXgC0UIbQ7FyVuglFFAJlJs3CpWHjPPfegMrt3707gQlX0yy+/yDTvv/8+Pl511VVDAGXO3ojMYeWpp54akvM07959990o6PXXXwcRQUeQUpZLdmJDB9TE5s5wkQrgGq/tlNVRsXD79u1YnWC82Lx5szwMwH46zk54BoChh0x1CfDT6uoquj5GHKU00WTM+cknn0TO3HvDX/yPsiDAkJyneRf0AnoYcNfW1lDiE088EZbrKoJ6HThwICEYuzTSEAqkxwmWTF8A13htp0XYzVXxQmLmjsEi3ExxZchlhFewtyURrnKiqxOuBJ080X0EJJCrk1mdLqRxYxW4SgOA4VYDl1nyIc5dqxMugcP0Etg0XNFWzu6yNbE6wWDxww8/ABq5jsP/WF5x3YcHY0248+kNQNrO8d90yITbsK4B8D+AG2srv0zK7rfuv/9+/HjmzJnHH3/cSwVNiYpw1xp/gfCbb76ZKB8TzY8//pitwO19jPJe+gK4xms7DZb/8TvhvoM9vRAwi/9ecLnEEjfVvLCsGHvLEFAiYCxUAmXJRkTAWDgiuJa1EgFjoRIoSzYiAsbCEcG1rJUIGAuVQFmyEREwFo4IrmWtRMBYqATKko2IgLFwRHAtayUCKhbSJVY+OEHv8nGMFkz/0V7GB/Q0VVajzWRwIvZwkx97odFmBWtJpWJhWBjsa2BnCpfbWnJYPkuNgMamxjN7oYU6DQuyLlHFFvbIPOtmUJx5xRchZ6/caL0S9VPulc+8J5a4lehC2g/Tm/P06dPsxN988w2+5IgDi0PvRguOyK678yMs5GAjeMEFF+B/abnICQASQ+O6IYzv4idZCl5v0AI8odVgzQrjfjjfPP/880ut/LzKF+hCviKd9aPWh7K7e9ZpzjBJCuPcH6Mm712m8LMyK9Tg5qkrogQKJhzw5l3D6eUfqguhfqDqDh06BExp4YebG2A8R1tD0gVYI0F6Ag5zOtrx4y1QFjnQOQh50sZMjsj4SCNkd0kFGhUUbNPpKdRzGCtuvvlmfA+ja6UL2BIpS02f7vLHoR119EIW7yqWqC6U/YaZSMUWzgupfZ1Xpb7bjZpSMy9EN6MDtbx0YVSp2s98qC7kLRagJu2o//zzT/y99NJLZd+lm9mXX36p7NAaxx94bKDonTt3YiqJmSX0MRSMMv8ZJsP0F9LCIhpG1JpqzlDUWRXdY3XiFNXvv/+OWfb01vb0OoAuvO222+AfvWfPnquvvrruRXpjNMPevXtBQYwb0gF0jILmN88eLOyq5Pr16/HTTz/9JBNwT/vaa6+tCw1mVNCIYB5YiE0iqMY33nijbhF1c8MqHvNjeD9V8b+pK1s7uVVgIa9IA9Zw/aR7IhYlDz30EP7h3QzFD6gmN2LQoijCjcKYCWBoLs58ghfRWwALprMvvPDCBMXNcRH61UliT6Rsp8abQQNEWYR09sNPSOx9Q9DDe9kmnphTtuiTpkXFGyknrnKV4iRuFXQhsoM6hHuiu1+QHo0HDx4c0juRg7ywEFk999xz0Cvuqj+QEitxG+mGgNzIu+YJOrQhzBO0DEHzBC3Dzd4aC4E6I/JY0lm+y4GAsXA52rntWlpk2rbbZ6Glo7UAHludDG1nW52UIWirkzLc7K2xELB54VjIWr56BIyFeqws5VgIGAvHQtby1SPQj4V0bUxfs64ve/qUMC+A/HboNz3ymRI11gxMQ3NoL54Wvk/HvlOefCNzeUYMy+So8QS+dOfIXgwpJ6R3nO0JwAgzFQ22kZuyjvS+Cx0LUfe0zMg/W3GlDO0kk7ipYj9RdMAnw4nxy+it3NGoEOn6R+1lvHBOLoaj61jOYcpRMLwCPowJFa1IcfMoWeiA8lgYNUfqW/Fi4Wf4YgkLu6L0stWdaqGmyQbNCysPhuFd55bBfPA4dzVqYhRHgyg6TOEb6elHjeLiiTKeHr7xnKbrRhzWsJDC86Z/j4VZmTUVnyGZiosuYWE0hiCb03PwZsrhbj7Ujs4Ij7EnPGtCGbSRG/FeB+gafzHiF3SVKOJZFlLbEaWQhVmZNRUvpsIMX5S4aVcnH330EejluTAyotVNN93khkj8wxB233//vfyy+H/n3XL8+HFksmXLFpkVPsJ/lPbY9DqFS4pMcOWVV+Jj6CR13333QUFO4DwF2eAACqmi1pYambMVL8a2nRdVLERrobHpThs+XgTGG264AWkYE7D4QYm4mCGcCF522WUyz1tuuQUf3f0Q+N9zBSSJw/sbKGStrtJVTfg/MAL3K6+8koBCI3O24sVQt/CiioX09aRemeBB4z322GOjXqNxxRVXDO8qaSjoAIo0H3zwgbnBp7FSsXAC5rkioAUZN2/UxpuAFlC0cADFc+GFF8rbdnj5jnePz5QIN1hWBRaePXtWVoyTxUsuuaSgtpgnYdzHXL6LgvTxcw/nTBdddJH7hqF+3cOJlzecFQg26isambMVH1XCsTMfxELOro4ePSql/Oqrr/CRQ16vB+ph69atONj4/PPPQ13FKSAvsnHPiRMnQFmSjFNA3AIjE3z33Xf4GN6I4DVqLzmViXnbjvfgXe7UMKauRuZsxZXyNJ3MwQQpu9bt3LKKnjdo9gu5T5a+sY/7Mgm3Ts22WXbvzVWQe0xVvEgTuCVY6H7Kyqyp+Aw3XIqLlrhpz054N01YpObsBOsMFJneQezqqXKPt9bZCWrBTbjhm5rcAtS3hNOF7hU7O/kHQ40uRJrorjXfTZ8jM24tiJhuKg0LyZ6B58gUY8pda1nxkIX41c6RtSwsPvXiFXJVxj69ykmnLK5LNNteurBWFRYgn5IRGdUuMwLApBCjeVOolVWkqwrGwrLGLWRhl2VXWgiMfaFVS5ncVd6aoWVXFfkXJhPJQvMEbXoHY7GF49oOj3mCDm1o8wQtQ9A8Qctws7fGQmDQ2clYQlm+S4aAsXDJGrzJ6hoLm2yWJROqHwtb9gSFgQLCmGHOO4EF9ZKRZPzqKk/weNAEcUbyBO0K7OP5g6ZP8HBaiPM9PFOG+FLuWtOkI7rbZyd42hO8rrMTjTWDZqNVw8KsNQMKqns6p5E8y0IZQjXM0KwZ/tk1VOrCsT1Bs+zRGzjVPaDLEjHNQhrvuCfMzSy7erBwbE/QLAv1DpET208MZCFeT3uv6iue7TBNJZC4aVcns/IEdVpE7xDJQF/vvPPO+JPqfAmwqWbbRy+fME9QIqhi4WSeoAht5+J8r6yshHb5SodINDncjvIcaSOFeYKqWDixJyi4AZf11dVVeFKWOYgg/h5yaINjJkUeARUL89kMTuH5CtF+G/psbW2tIO95Cd1dULWFfKUCCyt6gjqIMbfbv38/PnpekgvpEGmeoINYWNcT1OvlHrl7OUR67dqs/jBP0H+bRrNfOIEnKHYrYAXtrnjDiEwfU3dnl36/kAvSWldyZXc30js17nWukW2/MMo37a71TDxBPRdmzdkJK4n2jvqtZilVkKDXfiG7vjyWtLOTobvWbLMqnqDIxLtROOq2l/UEpTxo6cm8/gayEALbObJWF2bPNrq0yMSc4HAc3nxcoOSUryhHZGVuy5NM4qZlYXHrTuwJWtxbipvfWFgGXSEL2/cEbdmyq6ypFvitQhYCEZ6sp+89mhVwoKDmQpzq4pkuLINU4maeoEM3E80TtAxBiZt5xZdhaG9VQIB7anhMFw5F03RhGYLmFV+Gm701FgKDzpHHEsryXTIEjIVL1uBNVtdY2GSzLJlQ/VjYsle8puEsPrIGpRmkiVraRPcho2cnOCaG9YqLB4sz3DAsLeN3Mg3jEg73Wi+ONTyrWzTNK94jVeHZSdRKINpvJBHdkYZMmb1sPb0dPyTWcPGBeJdI2bMT84qPQlfCwi4rAVATnKB1qotZLElG3YNvmAZ/ec5WbHk1JNYw4ahr8ZBmoXnFa3qv1qYmEWki1LSyYWhjLONkl1lFsJSBsYadqJNFmsiyEOCYV7yWhV221iHTAasMlROizHObAot8UFmK4RUUDRke/dKZZUwZdSdq8a+ROezGnFR4fbvMpGCGb0lVpVojp73i5YTv8OHD+PjII4/ILzdu3OhNHwFiX3/hirGGIcw08ZGVi03zilexUOkVD7I+88wzWAIjoqKyAZTJqscaniA+srJqlgwIqFioQQpbcQgqC/4dPHhQk75XmuqxhieIj9yrgkueuA4LMRDv2LGji4LhLR+IVO3C2dVtAI2Hed0Sh+emkXkhrwNw0A1lIdAB+Xbu3Imdl6gW5MVFp06dckXyxl/u1yifWrGGXXFl198opdUnM6/4f7HSnJ10ecVjhQGVhnVrYrGp2S9k3FA8ckMnu3xDerkYR/rsjZQuz+njI5tXfIWzk+hOTdc1wOCHc/zWnJ3QW7SvH3vIQo2HObGYLD6yt1/IzmZe8dytO6cBNbrQqRnv/FfDQnemkjhH5hlreACdVochC7mtTY2IB3rau5x95rvWIQuVMmuuA8iOHk0lKGFh3VMvD46KJxkaoOvWRaKpKd3SEIESFnK/fow7DzgpxPRxsuapWxFjYVnDFbJwyPlvQlBOCofbeimxmJVll1K85UlWyEI3qW/TK17TfjQJ67sMyk5PNUVbGg8ByULzBNXv7sVTmidoGYLmFV+Gm71VGQGuUfCYLhyKrOnCMgTNK74MN3trLASGniOPJZflu0wIGAuXqbVbrauxsNWWWSa5+rFw3r3isy1rAeezEI2SQGnNwEP3cMs3ajOCZC5Oicaaoe+O7qge5n2vJZa7r15F6InsooHSLsmzgtOEJ+d5gbMLDjPpC2AL6QvPTqLHr1kWaiy79KBM42Hey9whwcIow8BFaUapYaE+0IseyZmnLGFhV8OQhVLzedXTWLkqEcn69matXPUBpPQWD2kWgkA4KOcpubsRALrcVTnLeL3MShgbSVbCwi6v+CwLK3rFZ1mIitXyMNeHaUmwMGxvck6aiGdZaLHiz81Eo7HiNRNVOjrJ6NqbNm3CiwVRtKeMuz5qwHlGllQ+x48fR8otW7bI9Ph45swZ6c2jzK3NZKo1ctYrfuvWrYzxvnnzZjrGy6eKV7wSvooe5mMEnD9w4AAqsn37dq86e/bsIYDAamVlJXTOkt0Y75LHp0+fVsLSeDIVC5Ve8dRw8MfbvXt349XWiFc94Dxcto8cOYJVs0cpKQzmjqurq9u2bWvES1AD1PA0KhYminGjJHdkADHWgIcOHaK751w/dQPOQ8PBZRv4eBdXeE6uDG2Jzry2tjbX6PUSfigLZWG48AAQP/300/iS6pNPa17xE3uYozgMDtBwIQXDpsJ8dP/+/fjec5WfWOZeHBqeuCYLKY0HXxWveE09q3uYVwk4jzEBwyvGYmy4KK/vOXv2rKwvp4DHjh2TX544cQJjTmJk1yDWUBrN2UmXVzx2GXiLJvfD8Je7g9JJSrNf2NcrfhoPc2XAedS3aweOEe8xwia8arCBAIjcPjZfQZ5uC9b2C8/B28srXt7Tqjk7UXrFT+xhDipoPFQSLOw6WJIkiyokz7PHzk7+JWJ015rLEXm7Ov4Pz1Gyt6srveKzLORhd9YrXnMmW2XXWsNCFASSuTNiKM7oXcsamRs5FFGKIXuv9i7X7Ba/suxosom94jWiVjnB0xS0tGlKWAiw9A3TC9npveKz4vXqcokROVvQMicoZOFieMVnG76iZVe2rGVOUMhCQNZyrPgqLVoQcN50YRnyEjeL0t3QrtmyiQL6ssrnWLhsEFh920Gg/tlJO3UzSeYFAWPhvLTUIstpLFzk1p2XuhkL56WlFlnOvwHTwAKR8SWryAAAAABJRU5ErkJggg==)
∴ It is clear that at (0, 200) Z has its maximum value i.e. 400
Also, Z is minimum at two pints (0, 50) and (20, 40)
Hence, the value of Z will be minimum at all points joining (0, 50) and (20, 40)
Question 9.Maximize Z = – x + 2y, subject to the constraints: x ≥ 3, x + y ≥ 5, x + 2y ≥ 6, y ≥ 0.
Answer:It is given in the question that,
Z = - x + 2y
We have to subject on the following equation:
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFEAAAAYCAMAAAC1BuGgAAAAAXNSR0IArs4c6QAAAJBQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjoAOjpmOmY6OmaQOma2OpCQOpDbZgAAZjoAZjo6ZjpmZmYAZpC2ZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm27aQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///bMnMDKwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABOUlEQVRIS+1T0VLCMBDMVYGIoBUEg2BRoiJJaf7/77yzRS5pAjPKg+NwD0zhenu7e4sQ5/qDDrw+nY6UlYCVRRGdeji0aDl4ibWtTE8dQXTvd9nkowW6RywAuhsNsN/AEJ2iLgry1Wyf5eV044MyjgW+7dHiX5zq4qRp27OeQ3/BMRkiDelb1vTg9cVKCN2LOOfm3h4r+xI69WGsvB7uJtCDpprXabWbtS+4HgUc3WwqStVMaV9UYEFPGFLOa7uUnUXwW0PuS2w1vidp3+XfGmUXXi7c21U2icERVE7+oKb6YVc+YpXfjPk+kchjQeysxE9HjwbYaYI8FryXjj5FplQkVmHWqhzYWIBoPEuEaB2v3lKO8KTxv1NIw8Sik+Z6pIMex6LzYzw0WQ0fT0oREWGQCMoveP7H0U9FARjDvmVRIwAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
(x, y) = (5, 0), (0, 5)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(x, y) = (6, 0), (3, 0)
![](data:image/png;base64,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)
We can clearly see that the feasible region is unbounded and the corner points of the feasible region are (3, 2), (4, 1) and (6, 0)
![](data:image/png;base64,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)
As per the table maximum value of Z is 1 but we can see that the feasible region is unbounded. Thus, 1 may or may not be the minimum value of Z
∴ We will plot the graph of inequality, ![](data:image/png;base64,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)
Here we will see is the resulting half plane has common points with the feasible region or not. As per the graph we can observe that the feasible region have some points in common with - x + 2y > 1.
Hence, there is no maximum value of Z
Question 10.Maximize Z = x + y, subject to x – y ≤ –1, –x + y ≤ 0, x, y ≥ 0.
Answer:It is given in the question that,
Z = x + y
We have to subject on the following equation:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARMAAAAYCAYAAADZGRnPAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAgOSURBVHhe7Vy7cuJIFL2inM8HkEoEnkk9VStvzgKJIwISIots0FQtGSUGho0IBm+0aCIStsqRJzBafwAEQ0q5ahAb+gP4AfWelgCDzUNCYm2YVggtqfvcvqfPfcBJtVolcQkEBAICgbAInIR9gLhfICAQEAhwBASZiH0gEBAIRIKAIJNIYBQPEQgIBASZiD0gEBAIRIKAIJNIYPT/kNzZG9aoX9Npu0eTTk3yf6cYuW8EDCPHrgp50s2++ypVbVK5XaSBsJOLB/BxgI/0FJ+UTLFarcZ+CjLhm2Rs3dJLOrGRO2OFfJqUCjeLRl2ZaLBv79jD812HO1fovswoPnhdZBjGzrN16dQkm/VIHlt0BXullXvqshYb1F7XWteZ9v3DnfOZslK5VKQ0nLwKJ49iG7hE8mtC0tkXGjk9Uv7l+GRcfG6dlmMYRuyoySQHB27k6yRVKqRq/JTpvcgpY+TesPPGCO9nVLo9J0WPwrziGTMEIrGz1SC9r1LTLlJnShxGWWN62qQbq0XxA4H7t1abZH5w5iF6+6rz0CxTKZMieaoedl4G8PnY/4WaPz5QQgJJdQbMKF86HzOm9M36izJpiU7OHioMeHkXZJ3dKxJd8Q3vST2tG/0JND8FvFfM3yuPr+gcnjYVmTBs8FCAK4CrRp2uIVUrdxo1y22qDjpAdsKJZGcsw9xY60ykJHYjf7/yhiI5KYLOR9h5M2LWDXcCjRKLijF1gU9MMm8sqm5gkzDYbvSFBHzB3S0guVGPdGW70qjVOjF+RzxZJdbOOdZtQ8orafCK6mjwhRJiEizRDUuC7CEXH6aRIkvuBnY9Cfhc0lcyv1kENqGTQbwqdTVOKJgw4kPOyobRZs3r/UlZLFgyejYDc5ArK0Fgs9Og19WYlB4GIhIjl2MAjeq6CQJRScuWqc1S7jMng04QzI52rLDzetN6Do34Uz0lBcOehZ/DEeVaBpvt0adPCoPtFl9wYqmh9MUnkTydV63DiSVOSTSmtnPvnVvIFSXdRy5Ic7LlEulpOVatbicVL8T5JLEpPs+QHNoIfchxw5xUy6bmEI6dv4JjG2wMZXKdtSm5x5iYg5jLqkzX78lemN14NMQBUQ6UnLQaCnEy1Lp8zlAhkwGI5BAzEvvlMmHnoPgqdKr6uycMttt8QU9IcPpqICXxdNadzvcY5Aox1vaSqOk8VzuOrhgh8ipTfKYzc8nEZcd2k10jxMgXrvFJmZJxHhqsv5ak3Ua8eRy6OlyRM1lSdX0ek3onxB0UUgpk4p8MUiWbuqdQJmmFTFVlXJmUip4y8bcV9rvOsHPg90eBdxR2riD/5F6IkXEtbPDDtnNYG+2C7eI71/nCF/iC3gLMtXAheg7KpJH/LLn5QxXhfxfKJIGwyYcy8YvNPAHL4/p2U2U8Odi0tzszl3Z+f9aDEujq+cgZyqo66bOYlCfBKEs2grogwQnkHHa2J+d605xJXuJxosaakHMIdXYmlUjW6dcaG8ZFNY+wdt5UzTlkO6+G3qZ7nsDTEr4OpqDYLr1zhS98hC/8gC8gi+nlKAJeCP8dC6FNfSF/aC/kTPz67/rXTvG5VCgRo8dqjmGgdHn+QJpmItFT+F/KYY/y7obOUH6zChIiHObLcOsWWOsMJC7nktUk4kRezcmT2e8zt5qDctnP3jMg7Px85/B9ePYOKstcDrlnI9VTZFIQOm+7wmC7yhcuy45XOQmgHnh+Y2wh6VpH/rByRxqqOTx/OEu6BhD88+XypO7ZW+ZI5r3EUxI8r7R4cXw457rKxDtt8m4jVVG+IDJRXy9cbMxgbwPW7/dysUyanqb61Sm9G2p00UICbLvdfD2+A2KJJxEn9tpen0n+nK+R/azNYsLO67eN4iZHnpSBrRt8woXJ9qagKLB97gsSmfPSia8tT/+g6Q59Jm4bAu8ziaNqE0X+UHnr4TMrA7v/NQB8voKDLxXZrTqdcBCsguIlXNHpx+VUCxUVM52mu6bNkpPdQwQ/y6/VBtKFRsxE7gTxFWHxO4cka9UKTh7+HSeWtVLcz2QjGzOk0Xj5YfMS4bsuSBzqKuJL2HkzoDNHNuteEUKmMTokcAajXaKUQtiNA26djfxg68e+T33BDKhK+Aq/x5Mx7HK3DSHKPxeRP5TpUs+Q+cefNEoVHcXIEZrYiP3SpN9TEkED0AkHzGspyVPW7rGibFFB8pJsfRS24eB7J5QU2IQfAeWiTIMdgsMokpMR++7S42Zt2m7vy/QbXQFfuMniNsX3TNjLvQzCzqtszR25ZaOpincpSzjYcPHQ2G49ti2sus8vtobPDbboC+kdkiXvHypOyiQfh5H/3hU+deATa41uHcpnpERsGZ9ZCHUySSKRmvRWyk9t7stxZGbmrDYJkgr1idiqYdoFiGQ3VRJVcjLE7DfeyuPhWR5nCvXj+Dm+XjJLK+MYjCrOm77FfT+amKKw8+xZaKXfDa5XbGeeb+PNXjOceKMjKoIL63xuI//YnjHf9p1itIuy+B6vIsfizzSTv4OpF+ATiyc/rcXnRdrpZ/EluTkaLidR8263ApWD/cF1OKOsQp0IfTKv7fcuYRA8NjuHsdG6e48JoxchE2+D9um6gTZcSpPO8wQ/+S8zB/GkFD/Kbt3jsXMYG22+9zgwekEyAZ2gaoTaFeJS3mAWUQknzFEq7t0LAsLO22E9BoxehEyW48yncel24MWIw0BA2Hm7nY4Joxchk+0QixECAYHAoSEgyOTQLCbmKxB4pQj8B8bg9KLlw4D4AAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(x, y) = (0, 1), (- 1, 0)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
(x, y) = (0, 0), (1, 1)
![](data:image/png;base64,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)
From the above graph it is clear that, there is no common region or say feasible region. Hence, for the given condition Z has no maximum value
Maximise Z = 3x + 4y subject to the constraints : x + y ≤ 4, x ≥ 0, y ≥ 0.
Answer:
It is given in the question that,
Z = 3x + 4y
We have to subject on the following equation:
x ≥ 0, y ≥ 0, x + y ≤ 4
(x, y) = (0, 4), (4, 0)
We can clearly see that Z is maximum at (0, 4). Hence, maximum value of Z will be 16
Question 2.
Minimise Z = – 3x + 4 y subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.
Answer:
It is given in the question that,
Z = - 3x + 4y
We have to subject on the following equation:
x +2y ≤ 8, 3x+2y ≤ 12, x ≥ 0, y ≤ 0
3x+2y ≤ 12
(x, y) = (0, 6), (4, 0)
x+2y ≤ 8
(x, y) = (0, 4), (8, 0)
We can clearly see that Z is minimum at (4, 0). Hence, minimum value of Z will be - 12
Question 3.
Maximise Z = 5x + 3y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0.
Answer:
It is given in the question that,
Z = 5x + 3y
We have to subject on the following equation:
3x +5y ≤ 15, 5x+2y ≤ 10, x ≥ 0, y ≤ 0
5x+2y ≤ 10
(x, y) = (0, 5), (2, 0)
(x, y) = (0, 3), (5, 0)
We can clearly see that Z is maximum at . Hence, maximum value of Z will be
Question 4.
Minimize Z = 3x + 5y such that x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0.
Answer:
It is given in the question that,
Z = 3x + 5y
We have to subject on the following equation:
x +3y ≥ 3, x+2y ≥ 2, x ≥ 0, y ≤ 0
x+y ≥ 2
(x, y) = (0, 2), (2, 0)
x+3y ≥ 3
(x, y) = (0, 1), (3, 0)
We can clearly see that the feasible region is unbounded and the corner points of the feasible region are
As per the table minimum value of Z is 7 but we can see that the feasible region is unbounded. Thus, 7 may or may not be the minimum value of Z
∴ We will plot the graph of inequality,
Here we will see is the resulting half plane has common points with the feasible region or not. As per the graph we can observe that the feasible region has no points in common with 3x + 5y < 7.
Hence, the minimum value of 7 is at
Question 5.
Maximize Z = 3x + 2y subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.
Answer:
It is given in the question that,
Z = 3x + 2y
We have to subject on the following equation:
x +2y ≤ 10, 3x+y ≤ 15, x, y ≥ 0
3x+y ≤ 15
(x, y) = (0, 15), (5, 0)
(x, y) = (0, 5), (10, 0)
We can clearly see that Z is maximum at (4, 3). Hence, maximum value of Z will be 18
Question 6.
Minimize Z = x + 2y subject to 2x + y ≥ 3, x + 2y ≥ 6, x, y ≥ 0. Show that the minimum of Z occurs at more than two points.
Answer:
It is given in the question that,
Z = x + 2y
We have to subject on the following equation:
(x, y) = (0, 3), (6, 0)
(x, y) = (0, 3), (1, 1)
As per the table minimum value of Z is 6 but we can see that the feasible region is unbounded. Thus, 6 may or may not be the minimum value of Z
∴ We will plot the graph of inequality,
Here we will see that there is no common point with the feasible region.
Hence, Z will be minimum on all points joining line (0, 3), (6, 0). Therefore, Z will be minimum on x + 2y = 6
Question 7.
Minimize and Maximize Z = 5x + 10 y subject to x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x, y ≥ 0.
Answer:
It is given in the question that,
Minimize and Maximize, Z = 5x + 10y
We have to subject on the following equation:
(x, y) = (0, 60), (120, 0)
(x, y) = (0, 0), (20, 10)
(x, y) = (60, 0), (0, 60)
∴ It is clear that at (60, 0) Z has its minimum value i.e. 300
Also, Z is minimum at two pints (60, 30) and (120, 0)
Hence, the value of Z will be maximum at all points joining (60, 30) and (120, 0)
Question 8.
Minimize and Maximize Z = x + 2y subject to x + 2y ≥ 100, 2x – y ≤ 0, 2x + y ≤ 200; x, y ≥ 0.
Answer:
It is given in the question that,
Minimize and Maximize, Z = x + 2y
We have to subject on the following equation:
(x, y) = (100, 0), (0, 200)
(x, y) = (0, 50), (100, 0)
(x, y) = (0, 0), (50, 100)
∴ It is clear that at (0, 200) Z has its maximum value i.e. 400
Also, Z is minimum at two pints (0, 50) and (20, 40)
Hence, the value of Z will be minimum at all points joining (0, 50) and (20, 40)
Question 9.
Maximize Z = – x + 2y, subject to the constraints: x ≥ 3, x + y ≥ 5, x + 2y ≥ 6, y ≥ 0.
Answer:
It is given in the question that,
Z = - x + 2y
We have to subject on the following equation:
(x, y) = (5, 0), (0, 5)
(x, y) = (6, 0), (3, 0)
We can clearly see that the feasible region is unbounded and the corner points of the feasible region are (3, 2), (4, 1) and (6, 0)
As per the table maximum value of Z is 1 but we can see that the feasible region is unbounded. Thus, 1 may or may not be the minimum value of Z
∴ We will plot the graph of inequality,
Here we will see is the resulting half plane has common points with the feasible region or not. As per the graph we can observe that the feasible region have some points in common with - x + 2y > 1.
Hence, there is no maximum value of Z
Question 10.
Maximize Z = x + y, subject to x – y ≤ –1, –x + y ≤ 0, x, y ≥ 0.
Answer:
It is given in the question that,
Z = x + y
We have to subject on the following equation:
(x, y) = (0, 1), (- 1, 0)
(x, y) = (0, 0), (1, 1)
From the above graph it is clear that, there is no common region or say feasible region. Hence, for the given condition Z has no maximum value
Exercise 12.2
Question 1.Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and Food Q costs Rs 80/kg. Food P contains 3 units/kg of Vitamin A and 5 units / kg of Vitamin B while food Q contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.
Answer:Let the mixture consists of x kg of food P and y kg of food Q. ∴ x ≥ 0 and y ≥ 0
According to given situation in the question, the information can be tabulated as follows:
![](data:image/png;base64,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)
The mixture must contain at least 8 units of vitamin A and 11 units of vitamin B.
∴ The constraints are:
3x + 4y ≥ 8 and
5x + 2y ≥ 11.
Where x ≥ 0 and y ≥ 0
Total cost of ‘Z’ of purchasing food is Z= 6ox+ 80y
The mathematical formulation of the given problem is: minimize Z= 6ox + 80y…….1
Subject to constraints
3x + 4y ≥ 8 and
5x + 2y ≥ 11.
Where x , y ≥ 0
![](data:image/png;base64,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)
The graphical representation shows the feasible region is unbounded.
The corner points of the feasible region are ![](data:image/png;base64,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)
The values of Z at these corner points are
![](data:image/png;base64,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)
As the feasible region is unbounded
∴ 160 may or may not be the minimum value of Z
But it can be seen that the feasible region has no common oint with 3x+4y <8
So the minimum cost of the mixture will be Rs160 at the line segment joining the points ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKYAAAAjCAMAAAApK4EuAAAAAXNSR0IArs4c6QAAALFQTFRFAAAA///b//+22///tv//tv/b/9u2/9uQ29u2ttv/kNv//7Zm27a227aQtrbb27ZmkLbbZrb/kLaQZrbb25Bm25A6tpA6ZpDbkJBmZpC2kJA6ZpCQOpDbtmY6kGaQkGZmtmYAZma2kGY6Oma2OmaQOmZmkDo6AGa2kDoAAGaQZjpmOjqQZjoAOjpmOjo6OjoAADqQADpmADo6ZgA6ZgAAOgBmOgA6OgAAAABmAAA6AAAA2/EaKwAAAAF0Uk5TAEDm2GYAAAM0SURBVHja7Vhrk9MgFIVQExu2xprG9ZFVbLRUW7XdjWbD//9hDq+ENEBZm3XGmeVTe3mcw73nXiAAPLXHbvHHubsTV+gfoATgJD9SX3fxfTYFyzMoZ3Giesn3umfss30/xWECf0qUUYM3NBCH8IFwW4K4Lq0DeN/FjVCbdfVlT8Nwkt+p3qx9KQDw/cVhlyi2UNEwHMkNbisU2+MyiTtdHhjQ9OAkjeTGtenMteJSd2oUP00PjuqJ9jmAW/pglMDmwadBOESmV9L4aEZ1GZTMjPpRLHoiX5ETB271tKhWK2fNSUGCa8Z289PxZ3h2KJjx1qoVOxS42DN27LOp4KNKCy/Vq/8mTelKmwOKtzpWJEicZsyKNgVg0dAhCmE5iGv3YgOc6Ns7TRMzhxowh+l6BejZZhYUoUbtnW4dkfAFcyp9gHOz7CTtpCn21QVrSDNr2PHVDsEbdkBZ0y61bW2ETBDS84coOIxmskMdTZebpB+iWgEPHFC0OcCMglWK79/kcqS2DWQa7/X0AYpHQQYO3KT9PD/NTtKmA4TQpAwLLn/uN8OmB/EMym2x9FU3AweXSnnmAky2EJrCGfLw4z/F0SFs2CDDwwVf25xhHjWnqAZOVItSkfp1ooM+1qasripDlA8Nm1kou+kGirs4D3GK0px3LoXKEU1hk2AifDy9DZtJxkaTUBRCM/k1M/XhFIoQc19IekcJSkKUMsrcb8K2Muq0XBZrS48i7pS4PFc31ZZX/QLlKNxUsjmg/lAwDju4pSh7X5fJJxllQuGHZ73NqLpZMzpEhKQhKV2xl3umYM1a4SUtzvFwbTGv84NRuGmvAWEVUopkx3lvU2yE/m/folNBEpkzLprC2knFeymwvQacR2rwdTMExYejq8jqJ2uvxRGVuwf9dRstoFCe81tuCI5KZrh5CTLnIHLpo81xE4zuhqgenP4953yvRPWFt2Lfq9FA9eF0ffE6fzDGpe9fXccDcFQnYbf5oznTTSGrQnH0q29hL/WTPNNdb8uiCsaBmwpFd6njRIKbapJPSBzF8uEIALwMxbmagVWjCtLoC9WLqb6oXc0sjzzG1IE8Hc5T+y/bHw8wc1GCSpXAAAAAAElFTkSuQmCC)
Question 2.One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.
Answer:let there be x cakes of first kind and y cakes of second kind.
∴ x≥ 0 and y ≥ 0.
The information given in the question can be complied in given form
![](data:image/png;base64,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)
200x + 100y ≤ 5000 ⇒ 2x+ y ≤ 50
& 25x + 50y ≤ 1000 ⇒ x +2y ≤ 40
Let Z be the total number of cakes that can be made
⇒ Z =X=y
Mathematical formulation of the given problem is
Maximize Z =x+y
Subject to constraint 2x+ y ≤ 50 and x +2y ≤ 40 where x, y ≥ 0
The graphical representation shows the feasible region determined by the system of constraints.
![](data:image/png;base64,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)
The corner points A(25, 0) , B( 20,10), 0(0,0) and C(0,20)
The values of z at these corner points are as follows
![](data:image/png;base64,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)
Thus, the maximum number of cakes that can be made are 30 (20 of one kind and 10 of other kind)
Question 3.A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time.
(i) What number of rackets and bats must be made if the factory is to work at full capacity?
(ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity.
Answer:Let the number of rackets and the number of bats to be made be x and y respectively.
The machine time available is not more than 42 hours.
∴ 1.5x +3y ≤ 42
The craftsman`s time is not available for more than 24 hours
∴ 3x + y ≤ 24
The factory is to work at full capacity
∴ 1.5x + 3y = 42
3x + y = 24
Where x and y ≥ 0
Solving the two equations we get x= 4 and y = 12
Thus 4 rackets and 12 bats must be made
(i) The given information can be complied in the tables form as follows
![](data:image/png;base64,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)
The profit on a racket is Rs 20 and on bat is Rs 10
Maximize, Z = 20x +10y ………………1
Subject to constraints
1.5x + 3y = 42
3x + y = 24
x, y ≥ 0
the feasible region determined by the system of constraints is:
![](data:image/png;base64,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)
The corner points are A(8,0) , B(4, 12) , C(0, 14) and O(0,0)
The values of Z at these corner points are as follows:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUoAAACvCAAAAAC+vMhcAAAAAXNSR0IArs4c6QAACp1JREFUeNrtnduBqyAQhv8WqIEW6IESrIEW7IAO7MAKrIAGbMAO6GHOAyDgJTGuOZs1w9sa3cgXLnNjBsTtogZGwCgZ5c1RgtvPWoHyjpPgv38Vo2SUjJJRMkpG+YsofacB6G56c//sLEi4nVtHIwFlw1sZAWH8n0I5ykpU+k2UOnzcEpFXAAD1l1B6CTUQkWvl/5l1PczeraYbiTrAE3VQE00K/fouiw9F2UEXdwwKgSxBTwZwDnZQaaa5BlA9ETlYpw8OYyxJqiezVsMRaUxENKKJf5NXwn84yvDOcz8BAD0RQQoAzkHMky5+2hE5qMMrQn3XKJ6RJA0iQpgjkEReCE9kMH76qEQxryeIgagXwhMBzUhEDrATOSGIvBAD0ahEunpigo9CTIuFc9n/EYaI4lzRICIHTT26j5/g5fzuwtLUYiCKK76DJSJqQNRjICIa4MihPbVWeiVGeozSK+UXKMnCCPP5a2U5Km3YWx3s3JeI0qLovUtXX0XpVfg1HrRRhgWgQkk6LrAOu4P5w9bKgyjtWZRma0OumktLaZwU8YfWkH8AZbmDVxN8hbLLQ+ocSlMsC9sT3M6CUrGDE1nY4i0/doLPcmUn47bTQfgtlBPk4MkP5uQErwTKTZQ6j9pSrnRoyeZv/FiUNIrcp1IYWqFMn55dK/FU20mf60rbmYRK0uaHoyRvgw7uFyL6CiW5RgBNT/8BZaGDKzFRki4/HOVfM9cwSrZXMkpGySgZJaNklIySUTJKRnkepas8Ptlw+NP+temvsQGkZZRn++d7gcqG0n7jBL8Cpc0mtQbGkxOY7oTSYrAyzTUrZ++YJbJw6aPHFp3XUQbreIeOXLRiankDlCK5ZMkAAMQ4owwfDRehzIM78nMwRFJ4Ihphb4BS9Z56IYh6qJG8hc4oe08dmuu2nRllAAedvCDmirn+6yhd2FodNaE7Cn6e4EREQr8VpYci8sGJcwuUFi710yaPQ/xIvxclGTiyT726jHIPZZuXTAdDUtJtUBpMexP8DSiLHZyIJIowlj+N0vq414RtxxTbTonSXYmykis7CPhboJwloLUwlFHaq+RKwC61HY/9kMu/hbJVUS7fENFnlN4IyPEylLUObk4P+U9cK3/VXCMlMcpL+ueu2XQYJVEjPKO8pH/TRZvOr6HkxoeYP3eCM0pGySgZJaN8GaV7em6O+tfMtF+FcsTsWPEynOoYGkBWR4gLpbl7STvZ9oPT1ErE32TW/P8+yhazEhwF9hjAXwzQypSjX1FPNv3gNIgUdJ7sUdMdUErVxrOYXoRIAoGeaFTF6KsMjK9E9W87byeBdkxzQjjy5gqV59dRDujG2JF0yikMl5JYZfYmJX+I0pSnP3siIiFugNLAkxLRsEBxBjsistmhWjquichiPNe/2iERL020PEz9R1F60czDUcS92WtIa0VfbOyFi5DIPT2s+BilQ2NE3GsK59xfR9mjJ5rCZppmtDfKSGi3h9KfOy5aoMyHoW6EMmzHGr5AqTQROb0+H5oC3H6MUo9Ekwn5HO6CckoDpM+EhsDQ58jAynF9Bcr4yyD9iHdYK7uEUmVC8ZhrgXKxg/90gqf/DHmnHVyKJDhO87YzQnSexgaGiAbIVUDkT7cdamAmmgzMjeTKMUXeDmizMBQUkJAaoEW3CtM9JwwVzttJZHXqLtpOO0MRskhE0CtAtp5i3MvScf0DET3q+5MRkNbfTQcvlGShV5c2Zt5JxfG7jGxrkWTYmMtnzRlfhTIZ2Qqz0TrD3A+MbF+Ekk2/16G8Qf8YJaNklIySUX4gSm4cfsUTnFEySkbJKL9LB18388i+8T0oox+1GZaWIa+2fYAqmjSHRgA6PNY8sKrn/K29BkS08ZaW5F8z/drz5/kfoEQ+gDuT3EI5zVl342PBN7k2Ga/7F79JTAv/xu85JC5HaYloMrA1kkZsHZfTKfyMSPcTeRMzRT/wYudvMoOnSaGtvW73Cb+KzoVwoisnmTZitI9RprEZxvA+CSwXY137gt/hvLUYWgnZUa8A44nIKsTlqChJYeG27g09tCF0ZDQCynkrIeyxUamVL8KvqMW4N9IWKNMYFYdR2jqa6x3hVym/dah/Y3L9maEqSRFRLu+tUIbVR8xRFwfWyjA0on28R0+HUHbp39tdEguUDaY6buYdgS4hgYoF2lj/IvW1qUpSRJTLeyuUaiDfQHQpH8uRbUfn6IwePR1COc6lHYb9tNLVX33MdP5ulC7HkIQvGIwWSJBiSYqIcnlvhbLoXNnzB2vlqNDPKPXD6gL5H/a5SIY7hrINo/j/oIyvqpG7lCpTBOG5QFneu0IZX/cgyjD4X0PZFXvNIZQ+FZEoo7neEX61wtND9a4o8iH/F0p6NE7SP/RNuQwfmeDjXCLm/Tv4Ak91YS5J8R6Ug0Kft53yfQbILZSTFGN189NtZygKQL1ZrtxAaYnGFroqSbGDUsHRZMUJlLE1pTBEZV6srpYrg2bkcsmYg8JQUa/n3drOCk8I9xLQVUmKHZThRU+j1D1VInp+H1UmrtlDeUREL1G+WQdf4xkVhJmgq5IUOyjJCqj+9QletYPhV1va7HPF8cuMbMfCr478BF+P8lD41bodMrKx6ZdNv+yQYJSMklEySkbJKBklo3yAkhsHBfIEZ5SMklEyyhuh9EK8bs9+eFTvm1D6LhS1nihbHnNJ6VUrfYspcPDRAdKdnGxF1OFtzoOPshCVohejKHS+IlmEXebAwQfHmrdzshUP3yYnm5ehtrprZUbSQU00qXWGDFfVP8iBgw8O228mEisevk9QYFfFAKVUgJiIaFwvgRXKMnBwPwXEDsr54ftkdKkCTLroo4lRBNjiM9OrAgf3E5NsZnQpHr5PTrYKVwopmGNrHqCsAwf30+Vsoiwevk/2qypcUuvDKBeBg/tJnLZQlg/fCKU8h3IZ7fYSyvLh+6Cs1qgZpXq6Vl6I8j452fQa5e4Ovhw+Jyd4+fB9dvBZruxk3nZKudKjHi/bKF/cdoqHb5TrN8bnAcjCUKntDOXYdGUcconyiDBUJhKjsljfbTJQext0cF8kuyt08LYMFNxFeVhEX6O8Z062LV36UCq7Q4rjdxnZ1kj8oaxhx8wZ32WvXIX3DUeqVR42sn0TSjb9XobyBv1jlIySUTJKRsko74ySG0ey8QRnlIySUTLKW6E8cMrRvJKu/6si2awCpIkOgXT2tqpkQosrzbmKeZeZyz8U5ezbCX6u6CWo6+ssrzw6/73fv+ucOJ+J0gtoRzQaYCwg1VWfVldeCACYv+lC1+JnopzTY1mYsr5oVYtsdcUfB1IktLjM4f2ZKHNUhEAOwFpUE11f0eLl/l0YsvaZKHMwiy4KvS3rNq6u2MNACpREFwUHfShKnbvq5tCfpyiHw0C+CGU9Ko+idIzy2Vo5o2xXa2V15RRKf++1crGDp5CCJzv4mQl++x3cC+ghyJVTkVe1lCJbmJWkeWLbub1cudB2UlhgqdsojCv954QwdHttZ6GDzwnussbtYwxwqZWfEdHvr4PXbUO7HjaiUM8ojl9nZFtDasUR4IxyTWmV4E61q5tOGtm+DCWbfq9D+ef7xygZJaNklIzyA1Fyuyr8itsfmwaMkhuj/N/tHwXXC36gNSDCAAAAAElFTkSuQmCC)
Thus the maximum profit of the factory is when it works to its full capacity is Rs200.
Question 4.A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?
Answer:let the number of packages of nuts produce be x
Let the number of bolts produced be y
The tabular representation of data given is as follows:
![](data:image/png;base64,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)
The system of constraints is given as
x + 3y ≤ 12
& 3y + x ≤ 12
Where x and y ≥ 0
We need to maximize the profit, so the function here will be maximizing Z
Maximize Z = 17.5x+ 7.5y
Subject to constraints
x + 3y ≤ 12
& 3y + x ≤ 12
Where x and y ≥ 0
The corner points are A(4 , 0) , B( 3,3) , C( 0 , 4) and O( 12, 0)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence the profit will be maximum if the company produces
Number of bolts – 3 packages
Number of nuts – 3 packages
Maximum profit is Rs 73.50
Question 5.A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit.
Answer:Let the factory manufacture x screws of type A and y screws of type B on each day.
∴ x and y ≥ 0
The tabular form of the given data in the question is
![](data:image/png;base64,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)
The profit on a package of screws A is Rs 7 and on package of screws B is Rs 10.
∴ the constraints are
4x+ 6y ≤ 240
And 6x + 3y ≤ 240 and x, y ≥ 0
And total profit is Z = 7x+ 10y
The mathematical formulation of the data is
Maximizing Z = 7x+ 10y
Subject to constraints
4x+ 6y ≤ 240
And 6x + 3y ≤ 240 and x, y ≥ 0
The feasible reason is determined by the system of constraints is:
![](data:image/png;base64,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)
The corner points are A(40, 0) , B( 30 , 20) , C ( 0 , 40)
The value of Z at these points is
![](data:image/png;base64,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)
The maximum value of Z is at point B(30, 20)
Therefore factory should produce 30 packages of screw A and 20 packages of screw B to get the maximum profit of Rs 410.
Question 6.A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?
Answer:let the cottage industry manufacture x number of pedestal lamps and y number of wooden shades.
∴ x and y ≥ 0
The given information can be represented in the following tabular form:
![](data:image/png;base64,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)
The profit on lamps is Rs 5 and that on the shades is Rs 3.
∴ The constraints are 2x + y ≤ 12
And 3x + 2y ≤ 20
x, y ≥ 0
Total profit, Z= 5x + 3y
The mathematical formulation of the given problem is
Maximize Z = 5x + 3y
Subject to constraints
2x + y ≤ 12
And 3x + 2y ≤ 20
x, y ≥ 0
the feasible region determined by the system of constraints can be represented graphically as
![](data:image/png;base64,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)
The corner points are A( 6,0) , B( 4,4) and C( 0,10)
The value of Z at the corner points are as follows
![](data:image/png;base64,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)
The maximum value of Z is 32 at B(4,4)
Thus the manufacturer should produce 4 pedestal lamps and 4 wooden shades ti maximize his profits of Rs 32.
Question 7.A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximize the profit?
Answer:Let the company manufacturer x souvenirs of type A and y souvenirs of type B
∴ x and y ≥ 0
The tabular representation of the given data is:
![](data:image/png;base64,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)
The profit on type A souvenirs is Rs 5 and that on type B souvenirs is Rs 6.
The constraints here are of the form:
5x+ 8y ≤ 200
And 10x+ 8y ≤ 240 or 5x + 4y ≤ 120
The function is to maximize the profit Z = 5x+ 6y
The mathematical formulation of the data
Maximise Z = 5x+ 6y
Subject to constraints
5x+ 8y ≤ 200
5x + 4y ≤ 120
x and y ≥ 0
The feasible region is determined by the system of constraints is as follows:
![](data:image/png;base64,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)
The corner points here are A( 24, 0) , B( 8, 20) and C( 0 , 25)
The value of Z at these corner points are :
![](data:image/png;base64,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)
The maximum value of Z is at the point (8, 20)
Thus the firm should produce 8 number of souvenirs of type A and 20 type B souvenirs each day in order to maximize its profit of Rs160.
Question 8.A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.
Answer:Let the merchant stock x number of desktop models and y number of portable models.
∴ x and y ≥ 0
According to the given condition
The cost of a desKtop model is Rs25000 and that of a portable model is Rs 40,000. The merchant can invest up to Rs 7000000
⇒ 25000x + 40000y ≤ 7000000
⇒ 5x + 8y ≤ 1400
The monthly demand of computers will not exceed 250 units.
⇒ x+ y ≤ 250
The profit on a desktop model is Rs 4500 and the profit on a portable model is Rs5000.
Total profit , Z = 4500x + 5000y
Thus the mathematical formulation of the data is
Maximize Z = 4500x + 5000y
Subject to constraints
5x + 8y ≤ 1400
x+ y ≤ 250
x and y ≥ 0
the feasible region by the system of constraints is as follows:
![](data:image/png;base64,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)
The cornet points are A(250,0) , B( 200,50) and C(0 ,175)
The value of Z at the given corners points are:
![](data:image/png;base64,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)
The maximum value of Z is Rs1150000 at ( 200,50)
Thus the merchant should stock 200 desktop models and 50 portable models to earn the maximum profit of Rs 11, 50, 000.
Question 9.A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods F1 and F2 are available. Food F1 costs Rs 4 per unit food and F2 costs Rs 6 per unit. One unit of food F1 contains 3 units of vitamin A and 4 units of minerals. One unit of food F2 contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.
Answer:let the diet contain x units of food F1 and y units of food F2.
∴ x and y ≥ 0
The tabular representation of the data is
![](data:image/png;base64,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)
The cost of food F1 is Rs 4/unit and the cost of food F2 is Rs 6 per unit.
The constraints here are
3x + 6y ≥ 80
4x+ 3y ≥ 100
x and y ≥ 0
Total cost of the diet Z= 4x+ 6y
The mathematical formulation of the given data is
maximize Z= 4x+ 6y
Subject to constraints
3x + 6y ≥ 80
4x+ 3y ≥ 100
x and y ≥ 0
the feasible region by the system of constraints is as follows:
![](data:image/png;base64,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)
It can be seen the feasible region is unbounded with
The corner points of the feasible region are A(![](data:image/png;base64,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)
The values of Z at the corner points are
![](data:image/png;base64,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)
As the feasible region is unbounded therefore 104 may or may not be the minimum value of Z.
For this we will draw a graph of inequality 4x+ 6y < 104
It can be seen that the feasible region has no common points with 4x+ 6y < 104
∴ the maximum cost of the mixture will be Rs104.
Question 10.There are two types of fertilisers F1 and F2. F1 consists of 10% nitrogen and 6% phosphoric acid and F2 consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs at least 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If F1 costs Rs 6/kg and F2 costs Rs 5/kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?
Answer:let the farmer buy x kf of fertilizer f1 and y kg of fertilizer f2
∴ x and y ≥ 0
The tabular representation of the data is as follows:
![](data:image/png;base64,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)
F1 consists of 10% nitrogen and F2 consists of 5% nitrogen. But the farmer requires at least 14 kg of nitrogen.
10% × x + 5% × y ≥ 14
![](data:image/png;base64,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)
2x+y ≥ 280
food F1 consists of 6% phosphoric acid and food F2 consists of 10% phosphoric acid. But the farmer requires at least 14kg of phosphoric acid
⇒ 6% × x + 10% of y ≥ 14
⇒ ![](data:image/png;base64,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)
3x + 56y ≥ 700
Total cost of fertilizers, Z= 6x+ 5y
The mathematical formulation of the given data is
Minimize, Z = 6x +5y
Subject to constraints
2x+y ≥ 280
3x + 56y ≥ 700
x and y ≥ 0
The feasible region determined by the system of constraint is:
![](data:image/png;base64,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)
It can be seen from the graph that the feasible region is unbounded
The corner points are ![](data:image/png;base64,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)
The value of Z at these points are:
![](data:image/png;base64,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)
As the feasible region is unbounded, 1000 may or may not be the minimum value
For this we will draw graph of inequality
6x+ 5y < 1000
It can be seen there is no common point between feasible region and 6x+ 5y < 1000
∴ 100 KG of fertilizer F1 and 80 kg of fertilizerF2 should be used to minimize the cost and the minimum cost is Rs 1000.
Question 11.The corner points of the feasible region determined by the following system of linear inequalities:
2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). Let
Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is
A. p =q B. p = 2q
C. p = 3q D. q = 3p
Answer:In the given question the constraints are
2x + y ≤ 10,
x + 3y ≤ 15,
and x, y ≥ 0
The function is to maximize Z = px + qy
The corner points are (0, 0), (5, 0), (3, 4) and (0, 5).
The value of Z at these points are
![](data:image/png;base64,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)
Since the maximum value of z occurs on (3, 4) and (0, 5)
Hence the value on (3, 4) = Value on (0, 5)
3p+ 4q = 5q
3p = q
∴ Value of Z will be maximum if q =3p
Hence D is the correct answer.
Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and Food Q costs Rs 80/kg. Food P contains 3 units/kg of Vitamin A and 5 units / kg of Vitamin B while food Q contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.
Answer:
Let the mixture consists of x kg of food P and y kg of food Q. ∴ x ≥ 0 and y ≥ 0
According to given situation in the question, the information can be tabulated as follows:
The mixture must contain at least 8 units of vitamin A and 11 units of vitamin B.
∴ The constraints are:
3x + 4y ≥ 8 and
5x + 2y ≥ 11.
Where x ≥ 0 and y ≥ 0
Total cost of ‘Z’ of purchasing food is Z= 6ox+ 80y
The mathematical formulation of the given problem is: minimize Z= 6ox + 80y…….1
Subject to constraints
3x + 4y ≥ 8 and
5x + 2y ≥ 11.
Where x , y ≥ 0
The graphical representation shows the feasible region is unbounded.
The corner points of the feasible region are
The values of Z at these corner points are
As the feasible region is unbounded
∴ 160 may or may not be the minimum value of Z
But it can be seen that the feasible region has no common oint with 3x+4y <8
So the minimum cost of the mixture will be Rs160 at the line segment joining the points
Question 2.
One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.
Answer:
let there be x cakes of first kind and y cakes of second kind.
∴ x≥ 0 and y ≥ 0.
The information given in the question can be complied in given form
200x + 100y ≤ 5000 ⇒ 2x+ y ≤ 50
& 25x + 50y ≤ 1000 ⇒ x +2y ≤ 40
Let Z be the total number of cakes that can be made
⇒ Z =X=y
Mathematical formulation of the given problem is
Maximize Z =x+y
Subject to constraint 2x+ y ≤ 50 and x +2y ≤ 40 where x, y ≥ 0
The graphical representation shows the feasible region determined by the system of constraints.
The corner points A(25, 0) , B( 20,10), 0(0,0) and C(0,20)
The values of z at these corner points are as follows
Thus, the maximum number of cakes that can be made are 30 (20 of one kind and 10 of other kind)
Question 3.
A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time.
(i) What number of rackets and bats must be made if the factory is to work at full capacity?
(ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity.
Answer:
Let the number of rackets and the number of bats to be made be x and y respectively.
The machine time available is not more than 42 hours.
∴ 1.5x +3y ≤ 42
The craftsman`s time is not available for more than 24 hours
∴ 3x + y ≤ 24
The factory is to work at full capacity
∴ 1.5x + 3y = 42
3x + y = 24
Where x and y ≥ 0
Solving the two equations we get x= 4 and y = 12
Thus 4 rackets and 12 bats must be made
(i) The given information can be complied in the tables form as follows
The profit on a racket is Rs 20 and on bat is Rs 10
Maximize, Z = 20x +10y ………………1
Subject to constraints
1.5x + 3y = 42
3x + y = 24
x, y ≥ 0
the feasible region determined by the system of constraints is:
The corner points are A(8,0) , B(4, 12) , C(0, 14) and O(0,0)
The values of Z at these corner points are as follows:
Thus the maximum profit of the factory is when it works to its full capacity is Rs200.
Question 4.
A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?
Answer:
let the number of packages of nuts produce be x
Let the number of bolts produced be y
The tabular representation of data given is as follows:
The system of constraints is given as
x + 3y ≤ 12
& 3y + x ≤ 12
Where x and y ≥ 0
We need to maximize the profit, so the function here will be maximizing Z
Maximize Z = 17.5x+ 7.5y
Subject to constraints
x + 3y ≤ 12
& 3y + x ≤ 12
Where x and y ≥ 0
The corner points are A(4 , 0) , B( 3,3) , C( 0 , 4) and O( 12, 0)
Hence the profit will be maximum if the company produces
Number of bolts – 3 packages
Number of nuts – 3 packages
Maximum profit is Rs 73.50
Question 5.
A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit.
Answer:
Let the factory manufacture x screws of type A and y screws of type B on each day.
∴ x and y ≥ 0
The tabular form of the given data in the question is
The profit on a package of screws A is Rs 7 and on package of screws B is Rs 10.
∴ the constraints are
4x+ 6y ≤ 240
And 6x + 3y ≤ 240 and x, y ≥ 0
And total profit is Z = 7x+ 10y
The mathematical formulation of the data is
Maximizing Z = 7x+ 10y
Subject to constraints
4x+ 6y ≤ 240
And 6x + 3y ≤ 240 and x, y ≥ 0
The feasible reason is determined by the system of constraints is:
The corner points are A(40, 0) , B( 30 , 20) , C ( 0 , 40)
The value of Z at these points is
The maximum value of Z is at point B(30, 20)
Therefore factory should produce 30 packages of screw A and 20 packages of screw B to get the maximum profit of Rs 410.
Question 6.
A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?
Answer:
let the cottage industry manufacture x number of pedestal lamps and y number of wooden shades.
∴ x and y ≥ 0
The given information can be represented in the following tabular form:
The profit on lamps is Rs 5 and that on the shades is Rs 3.
∴ The constraints are 2x + y ≤ 12
And 3x + 2y ≤ 20
x, y ≥ 0
Total profit, Z= 5x + 3y
The mathematical formulation of the given problem is
Maximize Z = 5x + 3y
Subject to constraints
2x + y ≤ 12
And 3x + 2y ≤ 20
x, y ≥ 0
the feasible region determined by the system of constraints can be represented graphically as
The corner points are A( 6,0) , B( 4,4) and C( 0,10)
The value of Z at the corner points are as follows
The maximum value of Z is 32 at B(4,4)
Thus the manufacturer should produce 4 pedestal lamps and 4 wooden shades ti maximize his profits of Rs 32.
Question 7.
A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximize the profit?
Answer:
Let the company manufacturer x souvenirs of type A and y souvenirs of type B
∴ x and y ≥ 0
The tabular representation of the given data is:
The profit on type A souvenirs is Rs 5 and that on type B souvenirs is Rs 6.
The constraints here are of the form:
5x+ 8y ≤ 200
And 10x+ 8y ≤ 240 or 5x + 4y ≤ 120
The function is to maximize the profit Z = 5x+ 6y
The mathematical formulation of the data
Maximise Z = 5x+ 6y
Subject to constraints
5x+ 8y ≤ 200
5x + 4y ≤ 120
x and y ≥ 0
The feasible region is determined by the system of constraints is as follows:
The corner points here are A( 24, 0) , B( 8, 20) and C( 0 , 25)
The value of Z at these corner points are :
The maximum value of Z is at the point (8, 20)
Thus the firm should produce 8 number of souvenirs of type A and 20 type B souvenirs each day in order to maximize its profit of Rs160.
Question 8.
A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.
Answer:
Let the merchant stock x number of desktop models and y number of portable models.
∴ x and y ≥ 0
According to the given condition
The cost of a desKtop model is Rs25000 and that of a portable model is Rs 40,000. The merchant can invest up to Rs 7000000
⇒ 25000x + 40000y ≤ 7000000
⇒ 5x + 8y ≤ 1400
The monthly demand of computers will not exceed 250 units.
⇒ x+ y ≤ 250
The profit on a desktop model is Rs 4500 and the profit on a portable model is Rs5000.
Total profit , Z = 4500x + 5000y
Thus the mathematical formulation of the data is
Maximize Z = 4500x + 5000y
Subject to constraints
5x + 8y ≤ 1400
x+ y ≤ 250
x and y ≥ 0
the feasible region by the system of constraints is as follows:
The cornet points are A(250,0) , B( 200,50) and C(0 ,175)
The value of Z at the given corners points are:
The maximum value of Z is Rs1150000 at ( 200,50)
Thus the merchant should stock 200 desktop models and 50 portable models to earn the maximum profit of Rs 11, 50, 000.
Question 9.
A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods F1 and F2 are available. Food F1 costs Rs 4 per unit food and F2 costs Rs 6 per unit. One unit of food F1 contains 3 units of vitamin A and 4 units of minerals. One unit of food F2 contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.
Answer:
let the diet contain x units of food F1 and y units of food F2.
∴ x and y ≥ 0
The tabular representation of the data is
The cost of food F1 is Rs 4/unit and the cost of food F2 is Rs 6 per unit.
The constraints here are
3x + 6y ≥ 80
4x+ 3y ≥ 100
x and y ≥ 0
Total cost of the diet Z= 4x+ 6y
The mathematical formulation of the given data is
maximize Z= 4x+ 6y
Subject to constraints
3x + 6y ≥ 80
4x+ 3y ≥ 100
x and y ≥ 0
the feasible region by the system of constraints is as follows:
It can be seen the feasible region is unbounded with
The corner points of the feasible region are A(
The values of Z at the corner points are
As the feasible region is unbounded therefore 104 may or may not be the minimum value of Z.
For this we will draw a graph of inequality 4x+ 6y < 104
It can be seen that the feasible region has no common points with 4x+ 6y < 104
∴ the maximum cost of the mixture will be Rs104.
Question 10.
There are two types of fertilisers F1 and F2. F1 consists of 10% nitrogen and 6% phosphoric acid and F2 consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs at least 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If F1 costs Rs 6/kg and F2 costs Rs 5/kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?
Answer:
let the farmer buy x kf of fertilizer f1 and y kg of fertilizer f2
∴ x and y ≥ 0
The tabular representation of the data is as follows:
F1 consists of 10% nitrogen and F2 consists of 5% nitrogen. But the farmer requires at least 14 kg of nitrogen.
10% × x + 5% × y ≥ 14
2x+y ≥ 280
food F1 consists of 6% phosphoric acid and food F2 consists of 10% phosphoric acid. But the farmer requires at least 14kg of phosphoric acid
⇒ 6% × x + 10% of y ≥ 14
⇒
3x + 56y ≥ 700
Total cost of fertilizers, Z= 6x+ 5y
The mathematical formulation of the given data is
Minimize, Z = 6x +5y
Subject to constraints
2x+y ≥ 280
3x + 56y ≥ 700
x and y ≥ 0
The feasible region determined by the system of constraint is:
It can be seen from the graph that the feasible region is unbounded
The corner points are
The value of Z at these points are:
As the feasible region is unbounded, 1000 may or may not be the minimum value
For this we will draw graph of inequality
6x+ 5y < 1000
It can be seen there is no common point between feasible region and 6x+ 5y < 1000
∴ 100 KG of fertilizer F1 and 80 kg of fertilizerF2 should be used to minimize the cost and the minimum cost is Rs 1000.
Question 11.
The corner points of the feasible region determined by the following system of linear inequalities:
2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). Let
Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is
A. p =q B. p = 2q
C. p = 3q D. q = 3p
Answer:
In the given question the constraints are
2x + y ≤ 10,
x + 3y ≤ 15,
and x, y ≥ 0
The function is to maximize Z = px + qy
The corner points are (0, 0), (5, 0), (3, 4) and (0, 5).
The value of Z at these points are
Since the maximum value of z occurs on (3, 4) and (0, 5)
Hence the value on (3, 4) = Value on (0, 5)
3p+ 4q = 5q
3p = q
∴ Value of Z will be maximum if q =3p
Hence D is the correct answer.
Miscellaneous Exercise
Question 1.Refer to Example 9. How many packets of each food should be used to maximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?
Answer:let x and y be the number of packets of food P and Q respectively. Obviously, x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Maximize Z = 6x + 3y ….(1)
Subject to the constraints,
12x + 3y ≥ 240 (constraint on calcium) i.e. 4x + y ≥ 80 …..(2)
4x + 20y ≥ 460 (constraint on iron) i.e. x + 5y ≥ 115 …..(3)
6x + 4y ≤ 300 (constraint on cholesterol) i.e. 3x + 2y ≤ 150 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
![](data:image/png;base64,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)
The coordinates of the corner points A(15,20),B(40,15), and C(2,72).
![](data:image/png;base64,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)
Now, we find the maximum value of Z. According to table the maximum value of Z = 285 at point B (40,15).
Hence, to get the maximum amount of vitamin A in the diet, the packets of food P should be 40 and the packets of food Q should be 15. The maximum amount of vitamin A will be 285.
Question 2.A farmer mixes two brands P and Q of cattle feed. Brand P, costing Rs 250 per bag, contains 3 units of nutritional element A, 2.5 units of element B and 2 units of element C. Brand Q costing Rs 200 per bag contains 1.5 units of nutritional element A, 11.25 units of element B, and 3 units of element C. The minimum requirements of nutrients A, B and C are 18 units, 45 units and 24 units respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag?
Answer:let x and y be the amount of two bands P and Q respectively which are mixed. Obviously, x ≥ 0, y ≥ 0.
The given information can be formulated in a table as:
![](data:image/png;base64,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)
Mathematical formulation of given problem is as follows:
Maximize Z = 250x + 200y ….(1)
Subject to the constraints,
3x + 1.5y ≥ 18 …..(2)
2.5x + 11.25y ≥ 45 …..(3)
2x + 3y ≥ 24 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5).
The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is unbounded.
![](data:image/png;base64,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)
The coordinates of the corner points A(18,0), B(9,2), C(3,6) and D(0,12).
![](data:image/png;base64,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)
As, feasible region is unbounded so 1950 may or may not be minimum value of Z.
So, 1950 is the minimum value of Z, if the open half plane is determined by 250x + 200y <1950 has no point in common with the feasible region. Otherwise z has no minimum value.
For this we will draw the graph of inequality 250x + 200y <1950 or 5x + 4y < 39. Here we find that 250x + 200y <1950 has no point in common with the feasible region. Hence the minimum value of Z is 1950 at C(3,6).
So, 3 and 6 be the amount of two bands P and Q respectively which are mixed to get minimum cost to Rs 1950.
Question 3.A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg food is given below:
![](data:image/png;base64,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)
One kg of food X costs Rs 16 and one kg of food Y costs Rs 20. Find the least cost of the mixture which will produce the required diet?
Answer:let x kg and y kg be amount of food X and Y respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Minimize Z = 16x + 20y ….(1)
Subject to the constraints,
x + 2y ≥ 10 …..(2)
x + y ≥ 6 …..(3)
3x + y ≥ 8 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is unbounded.
![](data:image/png;base64,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)
The coordinates of the corner points A(10,0),B(2,4), C(1,5)and D(0,8).
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAg8AAAB9CAIAAACqMhcWAAAAAXNSR0IArs4c6QAAIk9JREFUeF7tnd3LXcX1x+vvvsbaXIUSSjUXoUIlVi0SLyLEqoGiJLW1BQkk4BsUiuQFa+mFGt9qCyXk0dJAKKU2Uag3ja2B9KJVNL5QQfAithQpubLU+A/4+7RfGMbZ+8yevc/e5zln7+++eDjP3jNr1nzXzFozs2bWXPLpp59+zo8RMAJGwAgYgSwC/2d8jIARMAJGwAg0ImBr0QiRExgBI2AEjMDnLolXoi655BJDYgSMgBEwAkYgIBBsRGot7MZY6VaCvbcEV1qCZt4ILBUCsUrxStRSicbMGAEjYASWFAFbiyUVjNkyAkbACCwVArYWSyUOM2MEjIARWFIEbC2WVDBmywgYASOwVAjYWiyVOMzM+iPw1FNP4dn761//uv6sFHOwPDz/7ne/u/LKKwGQh9/FNXDCFUCgnbX497///dxzz91yyy1qDTz85s0//vGPFahrfyyq7uX0lqczW4LlUlNKtfbVMh5t69hXelC66667/v73v4vghx9+WKWsvjDr6R1nGjxlUeisOmLSvvvd7wZ+3n333b7Q6ECH0u+///5gbq+99tpaznkZ0sD84nhmw2V4qF78b/L7b3/72xVXXDELgkzG8X0SCOX1evLJJ0n/l7/8pTxLt5SWYDfc4lyJsL75zW8uRnbzcL6wBpZn8r777mvESqzOevrtI6is73znO5RFoVXOP/roI32Nn34ZaCtTNbbkeeihh2I6Ajl+vvCFL2Ch25ZVmD5WKaVzC0z07t274enrX//6H/7wh1AS4FKZjBXpYGCXP4uqv/x8xhxagt3k9cc//hFZb9++vVv2SeVijQH9kMfq4MGDVT31/PPPAxR6sEecmS5cffXVJ0+enCWCn/3sZ3xFd6HQsBziqkcGKDc/raky9pWvfOXZZ5/FyIkZfpPmyJEjdF4lZhqxtraGeZBVg21A+89//vPTn/50ES0tllxsRhKJim9MX6NFAnpajFhPTIs0LESwOsFCUm0e3mP/Q17gIEEQoQolWRgLQJkWFhstUSBNsM+1rIayyC4+a8sqqUWgr0qFgQz/wmcQeXW8oJEOteNHMLQki2vUiHNtgnWXYBV/yRqQ4Y3KUuVYrPFX0oBbGNxpEIogAkrKnlQ8xjCGXQ2mpF3FsoZCMpnQv6FQ/ateqkpVGzlfGULFVc73nUAzrhpckYt+p5cwFpqKgAoNjK/J3KJ2qlHlIdOhZjW/TL9ItFWJrlApMhXAmPT3bl0g7pWBpWqz0XIZkM4qVBgmGUsmT4lGrZ3WlFctaY3iKlEUtAce0VT6ZKqhjtBNvcSN/zPLKRldU8tEtc4SfPLEXEpC6kh6grWIX+pTPAWrpRz6kuAIVkrZM9aiWhbdL6QvqUXcGSirShBmYvnFmKgB1c46y5tRW2uxAAlW8UejZaCmo1a/BmDVMaoJgtBBoHZWHtSoWkWHdqVmGYsvsRYJzXgpgEolOEj0Ge2p9hbXS+aBl0GXVbtVXGgHa5HvULWtK98vEg4LrYVaSO+mIvAfRgxJjWrVbpIm0dS1Ysp3WDDpxVokzS8xBnHXFpNJobQlQO5mjGNFWmotyIOWz0Mjcw1bYakK1mX3kkZfOwZUJQUEMo4NptRKTJlGRgsLFlVtIqYwi9WgQeicoSx1b2mZwlok1oLsoVJarwsEoVkd61GWsggZ/gJaYQfLSGGWjSTLgiUYq1qgVjXDnFJQa8IaWjZfaTAYAOUVaJpEKntoTkoQxqSiprlarJerrWJWuwoDGniQms5bizCf0CQj1vXiASJqXZJs3lqQTBozSJZcZAlQVCWuUoKBaWstGjtUtcSSfpHMw/Lqgq8yFbHZC1mC7KpmUm8KHQyzrIVYBcBg2qsz14ASP8RqPKZsrJ063TzWQloibga1CCfSh89YV0twmbaUr0isUlpYi0Zdps6fzHeYH/Ay2A/1/4S/Womq08Z6IfaX8F6dUI1GFBJ3UC0KtWWJlORaWIvEWiTgiEiyqBK3b4kQKPp1T+WtxdASTPBXHZOX0oOCOqxW1456apdT1JyEpFpIAqA6vwgWtqtkUJ+UW7sSFTctdemgFOio1fWNRmuheiUL1nGDoUbAFRbKpDFDoW2thZDPdKhq3ynpF62shSZhqLZ4SW3B1kIwxk/SR9SEeAmrHSZAsYxKrEucRvgkhZZYi0TlJk2rLRuxSin1cpPngw8+qIIbv7l48SL/fulLX4pf3nrrrfz73nvvhZdf/OIX83T0ddu2bSGZtuLt2rUr3njHvwmdDRs2lFCuprn00kvDy8Ja5Av66le/mk+AOwtr/9Zbb6FZ2CfHtjl28gVfVrdaNOYaWoIJ/hcuXIAlfHSx1DZu3Bj43LlzJ50Brx0v2aj6ox/96PTp0/laxEV8/PHHJAbJOMu3v/1t/n3//fdn0am2q0Zh5Vn62te+FifAerG7sbCRh4z79u3jN5vR9eZXv/oVDSN4XPEeX3/99WxOxSv7pz/9qVHQjQkKO1RMp5d+EQjS1JE47f83v/lNAqDSUPe8XuvFHR2mrRp9YrqAN96QSilYYl4iVoTSKNb4dIE22R86dChu/5m9vDHa8IDEecMmi8ZCE3GrLf3iF7/gLzjTv+hltSA3tpMkQam1wKaB1xKeq3jttdfa1nlJ0h87doyRC5af1oBE0QU0teEMxlJJ8OzZs0iBir/55ptafaLi2BVGABjOJRHQItnA5iEgHWdDU6BGDxw4EBhgx4uWyNBoGok3LtR0Zn4xHerHP/4xdUT0t912W2dW58/IYYWgi+Hk8OHD0Ky1x+w7mr+4QgocOtmxYwema5apSLSEetOmTZtEX22JWqCuz5w5A+cPPvhgYdH5ZKXW4o477oBQvidr3Pevf/0rLvLll1/m36uuumoedkU5mThr6MGGvHkoK6943rx5M3+Hq0WVT0Yujz32mPZoYjboP5lB8ZzVXLwEP//5z8Nz7fIgVQ7VocdiODEbTL1p5RjOTE3/+c9/ho5x2WWX8TsZwbzwwgu83Lp1awlckvUnn3xSkrg8TTeTv3fvXjo2BuPUqVOUtWfPnlCi6sgnNFovg8QOHarHfoEaQco0DEQ/C1U0ZuYQ3/znJa+55hqKrj0MKD2ghwRMDrTDDQ3eKFn15fBAIfFbNOorJh833ngjyNAjqrOKm266CZrYgBi3c+fOwV48yaYtkeD48ePPPPMMnzI4l7fq/6ZM6jZr9kdP1ga+ZL8gYxwWNOVUqfrBtNaZeLmrq+e168taihU/Ybtb2Bkt5yFj0thvUeJQUlnBCanV89gV36EWEKxd7kz8FjF7fIL5uDq1y/TzLDImeRcvQRjQ/rewoUCDYvqeXAX85XdAKXiYxbkA4W/YCJA4satebjmcgywa25VcDjApHuQbgGFe5r3cCbaxUpA3JTj2KSLhKtPF5Eflb+KTTDbn0GySQ2dJ45EfLuyh0AaKGJnGDlVlsqRflPgtgrMq37YbJ09zerkl+njjjFaieBk8YfJyy88aHBitumTVWuSzC8DMVtfAdmixal1VJ7Z0Gp9KvLkZrmIbUWotIFe7GzKYJpXXdu+pcjX26lmUQ6+etfOhisKsVhhLqG0tGq1FUih9u5aNDm60qtrKCH7BEsy0GRlO6bjkSfZEJV8Tp2jJDtpkDBGPQuChepp3Tmuh/hw/Iti4xQBm4kNIsRyl/as0Z3m5q1uTqzzUNvLYTFYbUmO/KLEWVYnHbwptQInKri0ozij3b/LEekBO+GA8wvClpHSlaWstZoETN57Cs9yhdnPuo+loLai8NimqTejhdxhGCaBW59rKrYWMikZeKprfQbRtrQV544N+1TWuVrWo6gLxEzd9cNPkDP7lWwO3gCSfqqcRyxtlSBmLtjb7IiUoBrRrNpwsowfGG2pp02ELIz9iza7OGSdINl6LfgBWTSLeYFMyCgGQcJJOu3Xb7omqKgXKDZUSS4VaI8x1ajW1MNRGz3gXX7C7cXuDlFqXZiqaGVRnwLM61Ky2l+8Xq2UtqCPijiUVA5jsLBIgySSvsYcWyj3uv7UGIxFcps0HUrUSb2S4mqC7tehQ2LJlKbcry8Z5CT+N1qKEyJKk6WVpbhnqUm4tloFb89AjAm2tRY9FayKYWdQqLCtWKaVe7llTJL83AkYggwAbnPbv369xvYGaGgJo5Ea39kCYnDhxok//9v+4tLUYSFgmO10E4s08BLZjqxumope9TNPF1DVvgwBjFHbQakNwj4+tRY9gmpQR+C8C2IbgXZObId4xbIyMwNAI6JhnvAm7lxIvkY9OT6sbfnop3kSMgBEwAkZgmREINiK1FrHxWOYKmLdaBLD3lqDbhhEwAn0hEKsUr0T1harpGAEjYATGjICtxZil67oZASNgBPpCwNaiLyRNxwgYASMwZgRsLcYsXdfNCBgBI9AXAoNYC8WP5NqGxpCNfVVjFh0YgA2YiWPWD12o6RsBI2AExodAa2uB2tXho1nXeqCgiZfLNvPa4Ox8zeSFJjfJiD5RdgtVfCYXIX9hA2Z279697qZreVoP9w5ldksTH5sEsSASzruJaXmqb06MgBHogkAcLYT8jcFDFGxL10nWJs6E9yFgThJpOaZQGFsxKbQk17hjQ7WSYByUu1Z8IW5zaExJRLMSwBtbkRMYASOwEgjERqFFxHLVDSNB1MZZd70qVHJtcObYlFUvoiiP2x5DXJ5Lx2tr739eCZkVMpm390mE8CpN4laGmPi1tyWXA17IsJMZASOwzAh0txaKk0zEaWmN6hUcuv6o9pK7vLWQIksiJupCjwyU5bnE+fwRGZdZrjqX1whXEEQ1peYNuqooM3FsK6YlB83sGQEjMAuB7tZC2kQjdF0VkpShcPkZ6GctCilCZ3JxR+3LmHirXNCHvXE3i5K1RBCYdQ+B1hgzELUCfNxQu3ZGYAoIxCqlhZcbLzE3A6NwdVsscZi5Rvj06dPxpOGVV165+eabu/hP/pcnvlqWf3UJ7YULF/IEC3Oh6YgG2pm30WfUHcUMArg2+fLLL8/sNSgEfPSIuYJGYFIItLAWXB2Oebj99tsF0M6dO/n761//OsaLBNu2bVtOBLm3XfdJ+ckgcPLkybW1NeSoNPxLzO3ay+4NoxEwApNCoIW10PUaMhI8DDAZraNNVmVn6oYNGyYl2m6VRabBv61LUqFz9OjRbtScywgYgdEgUGot2IPP9RoMOTdu3Bgue+ENQDDn6AuOxPCcPXsWyps2bcrT75arL55HRofVv3BvDwOCY8eOaYYRV9OAj0zoro4RKEGg1FpkTMIzzzxTUlI+jVwUSSnnzp1jNpOsksd0WuW6ePHi/HyOmMLWrVupnSx08uD61ptWgI8YK1fNCEwQgVJr8fTTT9dudsLpjeuYmYewI80777zTAUdttsG/qiVyRq/8ZirDie6YmsJ44GzXy8JcSvz2228HrdeBw9FnYfMC0mS+CPISKH/5zY+wc6EV4KNHzBU0AtNCIN4ERs1r94TpdAUn8qpfdY4hfMrsoK2FNSbYeEiYnbsySK1yhcTknfgO2uR0niQSn5QMp/NiYbFLKj7V2CimKWwrdB2NwEQQiI1C0dzi1KlT5LnzzjurGv+2225DfYd17R07dlS31RaaX5bI0Vxh+I9m//Of/xwvQ73xxhuQSrRVYy6Vrp2+YUNXIUtTSwbazBRBWCe6w53S2jOtpxDwqUHn+hqB0SPQ802rrCBt2bLluuuuG+LaekLdHTlyhPFvxpMxS2C33HILXpDz58/Him980vVNq+OTqWtkBNYRgQFvWkUXHz58mLXvIXboc/SPCUcHUwEzsARj4zYV69ikXLQRMAKjR6DnuQV4Mb24/vrr+cHCUY/aGbJs3sVNwtpXK6kMxE8rHhaW2HOLhUHtgozAFBCIVUpqLaZQf9fRCBgBI2AEChHAn6+U/c8tCjlwsiEQ8NxiCFRN0whMFoEB/RaTxdQVNwJGwAiMG4GiHbTjhsC1MwJGwAgYgUYEbC0aIXICI2AEjIAR+JythRuBETACRsAINCMwiLXgfAO+EWI6DR3MnIBRFJTEkmqutFMYASNgBIxASwRKrYUMQPKgppO78ygdC7F3716CRnCcO5y3ePfdd4lPd+WVV4oChuSpp55qxSpkFVIwPvcHA1wiTdyR5557rhW1iSfmVDxIZkAAbRJUZaT7EzkYLzlyxR4iQLiLwTM0whBWMpQbPgWe9QZWy3lTpcrTO6URmBYCJVEFSaP7tGsfPsVEFLoueanYpclTG6awNlYXUe2IbafsCWXdMk1cozjy3UQCflWrCT75uoPS888/rzBQs1ISRJIz8ySIAw4qcW0zgFpyofpA+IfSq5eHqw3EPCsx78uZUQMrT++URmD0CMQ9onRuoY6UxCtVgL/XXnstmAHGnk888QRddPv27bFtIFwHk4BwKRu/+UrQp8KlqgceeCDc41a1Og8//DChDI8fPz7Lnvm9EGDczXn4u+66K1ykWkWGwTVXqybXH8XJEDon6mWbEQpWfMHg07ooN55ehMguMZ+0QDhsFa9MPd+txQgYgVoE2lmLxAB873vf4018g+mLL76I7vjBD36QFEbg0nvuuSdcysZvzTbef//9RsGwhEWEKOLRfvnLX65NjF5AZ/3yl79sJOUEcyIA1IiS4CtaY2QQ8POf/5wf3B0yJ+Xy7NzIRONhiBCyPProo7y54YYbYiJaiUoWpviXtVMtabKMRtOKxyvJypX+JT2rbVqk4gd3fujaD7LzhsXVeDEW+sliKSzNT7YcHKc0AgMi0GolKplb0EWTyw8y91skUzZZi8Z5HKtVJNOkpHaNSxT0KcxdGsmONUEJpFq7y6fUMk51JaqKW3nK+TEPZekHS2rQ1OUrvEk4qf1Xq1XxEy+H8j5euartdbUXaoWFuNomOj/Z+aEzBSPQDYFYUbSbWxw6dCg4uuk2BHZ98MEH49CBTALCPWsZE4dflLzVe3WSLKw2sFqFUgiTklk0Na4smakMaHgnSfro0aPUe8+ePfPUngE+jvdyCkxxwvSCDQ7Vlc9ZpJj4otCl3DEnGI+1tbV8uQyANAohF21ef1mL4w3LcWrDHa6mH4hsOYZOaQTaItDOWlSpswgebzuhN27bti3PBKph//79TEoeeeSRTEpMBcQxFSUbZHWn9Icffti2/k4/DwLICA8HMuoQRj4ulwEHLUe3uhY+rEShuFn5Qd3Hq1L57JiKgwcPiltMDiObjAtHcwLqqMEKueT8/+CDDxQIGba1GNv2yveByBZC52RGoBsC7axFsjTBmAulzyyhuqNxFjfMKhTPPN5fW5v4xIkTvMdghNkMMxve3HjjjdVtjj2GRu+G4wRzMRsoN+eN+DB0YGLKyKBw44OmFzSJ8olFlYfGkU2SRS663u9uGYhsI+ZOYARaIdDOWiSkGXPJyfnSSy+VlEo34ypWpv+NpqKEmtOsFwIodOYBWiRsnPnJ8dv4sFmLuQIzlfITEppSlE8s1gsul2sExoHAXNaiFQRoDaYFKJc333yzZCqARUncMrELMSm6cEDaimEnrkWA2SEKndkkM8tGUwEFVn5K3Gv4ABhG4AYo3/OqPbLJXm1LzQgYgYEQmMtasHfwhz/8IZzdfvvt4o8O/84771R5Rb+waMBQlP2Xs2oCNW1J7FBV+bc3b97cIa+zlCOAjJgdkp4bzhu3HpSTJSVHamgbPCUjiVaUF5n4qquuojg8/xq+AFf5VGmRfLosI9ABgXbWIt4ThWbftWvXW2+9hesvjDFxG7L6XOUD3wYvYyeElibivvTqq6+S5sCBAx2qoROC8nX7mYVAWBSSOCSCJLyHXjILJEEQdyD43nvv4RZG6CwcJYtL86zmc4IBF0LJTGXJhYtPjgET62nChw5y7ty5JefZ7BmBQgTaWYuEKA5Gpguxi5uBJ9qkGjyqhBuZmW57MV944QX2NfY72i3h2Wl6QYDtRixY9UJqfYkwMeIYqY6zaGENy7q+LLl0I9AXAj3ftMoEfMuWLdddd1356rNqQkaGY/SuzFLVrDozqmUsrM2RfeGyonQYzzp2xYrKzmwbgSVEIFYpc80tqnVjbHX48GEWOtquS7zxxhtQIyJIB7wI/MA4bt++fR3yOosRMAJGwAiUINCztaBItDaLQgQtb7VPCacFRzc6LCVxlBfj9Pjjj6+0d7REVE5jBIyAEVhHBHpeiVJNtDSE9h/6XIXOe+NmLz8euI5YL6Bor0QtAGQXYQSmg0CsUlJrMR0UXFMjYASMgBFoRCC4QgeZWzQW7wQDIeC5xUDAmqwRmCYCA3q5pwmoa20EjIARGD0C/Xu5Rw+ZK2gEjIARmCACthYTFLqrbASMgBFojYCtRWvInMEIGAEjMEEEBrEWnLTg1mIe4pUOiin0KYVAhK3OdgzKkokbASNgBEaJQDtrgVLmNByhAENEOX7zhqhwMTrEEyVaFAFzak/bXXvtteWBOWvvRQjZoU8p3ItAiaMUz0CV4iKj6o1ScVkIuhpwME7AAReCAAbpDD0sGAgHkzUCRqAFAvHdA2TLXEXAfQa1V9irsJCR6475N7llT19R67qjgrBrJXcezAp5lGSP770oJDvWZHkJ6ippAkESKCWTEkHrStFaIUJBX+MHoY8VUtfLCEwZgVhRfMY8ZDQIOkKmghPausJeD2rioYce4lN4gypHGZE+gViBOfW0shaNiXWRTmOyKYg8by1kVsNTC0icoNZaIG7SIHGaQVXKUwDZdTQC00EgVimlK1EvvvgiMwM0Mjff6Qp7Pdxc9thjj3Gvvf5lRYKoTYSSXWTUJsqiRMpNFsQ+O/z1fz0gAMJcsIqpIAokzWCRUu6Be5MwAkZgDgRKrcXvf/97SmkMJ/7666+T7M4776yyFG5OnYPbmVlvvfVWvp05c2YI4qOhGS49jed5Se3ClLG21gwaeE/QX9uJ0bQKV8QIFCJQai0YuTOi5NaaPF18ziwKdQglmyFL0fKmsv3p/vvvr3Wo6nJm+1oLpd452dmzZ8l78eJFtipIKGxIS27f60zcGY2AEVhmBEqtBXUouTH7448/5iqkgSrMPqu1tTWu56u1CjhUvBI1EPIJ2XvvvTdcCcf6JBeylm9yWwyHLsUIGIHeEWhhLYJzoncmMgRjb5L26mAzuM2imsVrIwuTC7uqgn8bXzezSeZ/ntgtDH8XZATWBYFSa8FKN6PI9R28s8CleyyYwawLWC5UCHDSIthmfN3clshLDIbxMQJGYMQIlFqLO+64AxRwG6wvFpkz2z7OvQDRXHPNNZRSe43u5s2bF8CAizACRmC9ECi1Fnv27MHLzfgR9+bp06cDuygOznIHl8Zll1127ty5bpXR+WGeMINhDMup47DEwQ+tj990003VIlhJb3TCd2PMuQIC2u32rW99K7QBfjzxxBO8HM5fZfyNgBFYCgRixwAMZU6d4DbQGeDaRxmfffZZvpKySqd212Z8BpgVcPLimYgP+lXLwptdPRSmA+SUPp1TM7PO1mUQSE7nCdvkCF5GuKKs03nJgydj4si7+kZglAjERqF0bkEe3Abnz59HuSSnstHRqG+pj2984xv8PXXqVAdL+Oqrr5Lr7rvvDnkpC92EedAbJje8qb3r++WXXybBzp07O5TrLK0Q4DAmtiEIBeuOqWYW2IqIExsBI7ByCPR/0yqLRSxGYVfablJijYv9Th12XrGEtWXLFlZCMCQrJ4B+GfZNq/3iaWpGYOIIDHvT6sMPP4zSP378eCuU0fg4Hg4cONAqlxJTFiVSboe8zmIEjIARMAIlCPQ/t6BU1iVOnjyJ96L8UDfO0l27drGi1XZGguv76quvZj1Em2sn/nhuMfEG4OobgX4RiFVKai36LcnUjIARMAJGYKURwHsv/geZW6w0NCvNvOcWKy0+M28Elg2BYf0Wy1Zb82MEjIARMALzI9BiB+38hZmCETACRsAIrCgCthYrKjizbQSMgBFYKAK2FguF24UZASNgBFYUgQGtBcf08JAMvbGVgxq6mccRs1e0CZptI2AEVgKBUmtB9ECF/AsPOpqQtLXhSKk5oQYJQUhQkCQmBPesEYJQRPhUouKxB8QWDLkwQnFYQ85ncISboCC7d+92GNrCNgee4D8rMVEdY8CrUT06CLGQMSczAkZgeREojCqosH21z3333ZeE0+KQHfEHCSeVvCdlQoFkXJuRicYFqRCSKM6bhLETe0mAvFEG+cpXChDyCcAT6BQdsjalbjeKoU7k2EGIExSEq2wExoFArCg+ozIyuqaqjnlDyD9pFn7E0CjWaRxflq8c7eYl6fUetSW9UzU2MSkFtdVdTMqlN9BJhEEaXlbD045DZoW1yFuLJAZtlSYgB4HWBhLuJsRC5p3MCBiBZUOgH2uhWoUw5rFyQeMwIUiqLVWVzAlIWdX7jYZHQXAT+gp4PvHQ2XNaC9nvTOD3bkJctg5gfoyAEShEIFYppX6LWctQRII6duwYX0OUclwRxPjbv39/kuXs2bO8Se7M4V8SZy5wveGGG8j129/+Nvgk+EGM2+p6CFd+kvKll16axarfHzx4UE2k9q4R8FlbW8MDdM8998zCqpsQjbwRMAIjQGBeawEEulXi7bffFhyvv/46f3XRRfVJrrfTLXgXLlyYBeX27duZLrCxauPGjTjVcZ7j5cbGPPLII9UsKEEC2Y5AKutSBW1YYFIIzpdffnlmJ0JbIa5LdVyoETAC/SLQg7VIosZevHgRFsujzzbW59JLL0V54RphCnLvvfeytl570yp0uDWar40EnSCDAMGDmWEw4VMa/iXE76ydb0bSCBiB6SDQg7UYdN+qIpmfOHGCK9vYKYsT+/Dhw1wErQu6k2fDhg3TkdxANWV+FlxQmF6t+B09enSg4kzWCBiBVUGgB2tx5swZjetL6pyYFq2Db9q0aVben/zkJ6yNsB6lBMxjWHxHhbHi5AFvCeBt0zBvC/NCVpzklGKGEdNpK8S2PDi9ETACS4jAvNYCnzbL3FRs3759+epp+UimJTz4q9kTlayDxwmwCoxwC6cvWgTz0w2BrVu3klH2O3lwfetNNyF248e5jIARWCoEulsLhvac6d2xYwdr3DgVgsbXclD1kLb24YTj3xgAfpM3OSqsMB4hXgiX4pHm+9//vgiSi08srPO7OiPB0x702lKhvBLMMG8DbU7gIxftUuOvhgI333yzqlAoxJWor5k0AkagHQLxrltyztqEmznLnRzN0wGu2j37jceAcUuQNz6BEc5zJLWqpU8a9F3hPuJRJstIkPomp/MEaXwAPpzOi9FmJTA+89goxFEC60oZgWkiEKuUdme5EyWC4kgObAvQ2tN5+oRuCsN/NHtyYFgn7BLzI19rCEdBLpJVJefTeWAyp7WAQow2kkJe1ePxeSFOs1O51kZglAjEKmWQm1ZZoTp06BCGJHinC+c7BLM7cuQICivjyZhFil1SeEHOnz+f7OgtLHocyXzT6jjk6FoYgSVBYPCbVvF4MxV49NFH21b4lVdeYerQwVTgRGHBnc21UzYVbdF2eiNgBIxAOQLdvdyZMlDZjz/+OOqbo9flrODBZgfU3XffXZ5FKcm4d+9elk0a92W1pez0RsAIGAEjIAQGWYkSaZaGMBjE7ahekNAj+pgKCsLM4ALp8QB5jxwukpRXohaJtssyAqNHIFYpqbUYfeVdQSNgBIyAEShHQNtn0rlFeX6nNAJGwAgYgUkhMIjfYlIIurJGwAgYgSkgYGsxBSm7jkbACBiBeRH4fw69AJY9fo/yAAAAAElFTkSuQmCC)
As, feasible region is unbounded so 112 may or may not be minimum value of Z.
So, 112 is the minimum value of Z, if the open half plane is determined by 16x + 20y <112 has no point in common with the feasible region. Otherwise z has no minimum value.
For this we will draw the graph of inequality 16x + 20y <112 or 4x + 5y<28. Here we find that 16x + 20y <112 has no point in common with the feasible region. Hence the minimum value of Z is 112 at B(2,4).
So, 2kg and 4kg be the amount of two foods P and Q respectively which are mixed to get minimum cost to Rs 112.
Question 4.A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:
![](data:image/png;base64,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)
Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.
Answer:let x and y be the number of toys manufactured per day of type A and B respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Maximize Z = 7.5x + 5y ….(1)
Subject to the constraints,
2x + y ≤ 60 …..(2)
x ≤ 60 …..(3)
2x + 3y ≤ 120 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
![](data:image/png;base64,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)
The coordinates of the corner points A(20,0),B(20,20), C(15,30)and D(0,40).
![](data:image/png;base64,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)
Now, we find the maximum value of Z. According to table the maximum value of Z = 262.5 at point C (15,30).
Hence, 15 and 20 be the number of toys manufactured per day of type A and B respectively to get the maximum profit.
Question 5.An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. What is the maximum profit?
Answer:let x and y be the number of tickets of executive class and economy class respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Maximize Z = 1000x + 600y ….(1)
Subject to the constraints,
x + y ≤ 200 …..(2)
x ≥ 20 …..(3)
y - 4x ≥ 0 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAR4AAAEwCAYAAABhbx6QAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAB8BSURBVHja7Z3Bjhs3moDnBXZfIOlDY3zYva1spWMg8KkVtY/TaCttH8aHjiYG0sFeBMPALgwrl/geuPMANjCbHMcvsDPzAIHfwP0GfgRNU2pKLIqsIllkFavqO/xAt1r9iyz+/PTzJ/n/f/jxxx//gCAI0qQkVf7ixYt/O//i4J93Dg9WQr48X/yPeP3VfHK6eW1y/d+vXn3GQCAI4Ikqr179+bOTw8+v/3hy8Vf19fl09MtssTxiEBAE8CSRxeze/6rejYDRdPzo3XcvXvw7g4AggCep1/Nw/upULrXkzwiCAJ6kXs8fv3j0zxevXnz2eHz8jtgOggCexrye6TePfvpy+u0VDx9BAE8j8peTg7/eORx9qgoqLxezoy8PDz7J3TApwmOyxYWERyV2zXY7Zjfv1wLa6i5bma5dG0Yf1bZKeG70F/th0y3bhbEhSEvgEZP5aDx77xJUlhNZxoLk7zpMtsu4m9fXsLj1piS81EkvwCd/l/9j9M628NrBRX5+4f8VwJTpVv+GIEgL4JmeLy5d3quDZweE4tkf8Zqc5IuLi2MVaiocNiA6/qDurJ0cHv/DFmva/H30QYJH/13V56JbwIeAOoK0AJ7F+eypa1DZBB4xeVVPwvQe3XOR4FF/dvpfDTTbz7/VoS6hXHT7eHsIAngiiZjID6cXr13fr596NsVsdE/DFvcxLX9CwKPGeNSlk4tukz4EATypvJz14UH/6xE2j6dwEFHzNHRwqIcUY4Bn14Zif1x0V30eggCeDMQe4zlYqQcRbeCZTyev92JBEZZa8v3qsstFN+BBkI6CR+5UVYFHeCD6BNeXZVXLtLJgsv53F92AB0EigEd4HiH/4/p/tu10dYljmuACRmr8Rb2eoW95l21xm3e1Pr8u3rDftaVKNzEeBInk8egH/GKBx3aA0HZoT4JlF09SZQeHwiE/JSazvUFf2Hrffb7UX3y95ACh4XwQu1oIkgg8ZSDyhZSrlMV5fMVnu99XOMeDIA2Ax+W9sTpRdgrZZ1mX6nQxJ5cRpAHwhL6vrueT4+TmrhaCRAaPK1R8PCMEQQBPbfD4xIEQBAE8XuAxgcb2fh48ggCerYTkshG/669XxXtidwKYIUhHwROay8b2elm8JzZ0AA+CdBQ8Ibls5s9np2V5aGwxnxTgaRM+wA9Baiy19GVX1SXIk68nb6suR+pgiDlBcwhUEyhHkIjgccllczS++7tLqolUgGh7l4wdOgSJCB7XXDah4IkxUdveoudoAIJEBo/MZfPbr/+3WsvydHXnq2erK/n7rz+vLr86WM3OLK8v5e8bsQFCfY+PVJ0NCtUb4/NTfzaCxJRswKPmspENs+Wb0YPLVTluUsREUngbVQMS4m3FHuQURtMFnbQxb51B4NHvOwlPpyqXjU+OmxRxkTbAE7LcwrhpI+AxgMecy+Z0VZXLpioPjWmyxvR8cgAPxk2/GZsIMZ6UDfO5XpEzeHzbjnHTRsCTCXhiwKdt8GDc9Jux6SB46sIH8DCpaSPgCQJPHfgAHiY1bQQ8UcDjM6Hb3k7HuOk3Y9Nh8IRO6DbBg3HTb8amB+AJgQ/gYVLTRsBTGzy+8Ok6eEIL/Zn02ZK1MalpI+Dx9GRcPaSmBiQ0CG7TKU5+68UBQ/XZkrIxqWkj4AmI37jEhboIHnFFZTqfX8bweGzJ2nwKFDKpAQ/gcZzobYFnN7k/v1ZLJe/KHO9KJ5t0iv99OL14rS611KWS8ILOFxd/2ujf94j29FmStflUL2VSAx7A4wifNsGz8zRGH1UwPJ9NfqgChUw9YorxiCWThMh8OvpF/m2zLLPfjHfJjcSkpo2AJwJ82gaPHk8RE/7x9NFPemBX1Sm8EwkEE3hUz8cGDr2NtmRtgIc2dgI86je4bFhxSVF0+313UmJcCDVdNG1iQGzwU+Gxjtt88+inzXLrYOUjKiTkkk19rdLjYalFG7sInl1drQ1cRMOkARd2SxQD991JiZnytC3wmP62Tity7/jDyXjyN1NA12c7XaaeXcwnT/VYkU2fLVkbwWXa2AmPR50IomH6xFANOmQnJWbyr1T5jkPAI71CWyI0V/Doz1CN91Tp803KxqQGPNmCRzd+1aBDdlJipzxNAZ8Q8AgxBZV9wKPHdnY7ZPvL2MoDhJ5neJjUgCc78KgxHvVb1DWgmaoaRJPgqfoc0fcn5/NLjJt+A54I4JGyPNulQ13evnb1/f3VnbOXStb6ZqpM2HQ2UVnC+p7l6V6/EYQqEzWXWmrS96oKo215PLG8njKPxxRXcVna8K1KG/F4PMBjDiBv/h6yk5Kydnos+PiAB+Om34xNAvDouzWbLffdFm9IeZsU4PnH3/8/Gnz0AYmhF+OmjYDHAh51F0WIiFnsv15ygNCjvE0XwYNx02/GJpHHk7phKcETCz6Ah0nN2AAeL/DEgA/gYVIzNoDHGzx14aP2O9XyDeOmjYCnh+CpAx8TeDBu+s3YAB4n8ITCB/AwqRkbwFMLPCHwATxMasYG8NQGjy98AA+TmrEBPFHA4wMf2e/Up6ExbtoIeAYAHlf46ODBuOk3YwN4aoHHBT6+4NFPfJtSkarP0nS1pCr3clU+HlPS+f32bU6d2/QKnSEJxJjUgAfwRIBPiMej38yXv8trJFKnLT2sqbBfWVpZPXm86TqL/D9XvWo2gljwATyAB/A4wkfP9xMCnh0QNhdq1xduRRoRA3RMhf2q0sqa6nTt5W7WLvRW6VV1qqlQmNSAJzl4TFUmQtz2LoDHBh8VPK7tMIFnnbto6038vDLlKjIV9pPQKMt1VAUe+f6Trydv1SoWZXpVnWKcj8az977115nUgMcbPKYqE6Fue1fAY4JPHfDYCuz99ubZypSryFbYryqtbBV4pGcjPKnd2E2uz7+5e2XTW1i+GTwoJjXgSebxmDIQhrjtXQKPDp+YHs92qbU83fMIywr71QWP7tnIvEpH47u/u4AnpC4XkxrwRAVPiNveNfDo8IkBHulBrie1Bh6Th+TzbH3Bo46hy1IL8ACeVsGzlptlwoNDkcz85S7J+83vl47J3vWk6SmSsKcCj3t7DX1fP7fb127Ac+erZ6sr6/+/XM0O768u3xSf+fJXy+++/79u383fl656q8cSIdl7Uo8nxG03eSUpErM3AZ4Qj2fn0dwutSwxnrKYSllaWdfgshwfdQxteonx4PFkDR4Xt72LSy0TfFzaYDtAqAbibbtaZRPdllZWvHem7CLqn1+MG8ma97v4nE0vu1qAJyvw6EHkteGOR++fzM8uc6kyEQs8ofBxGWQd4HX1Lc5nT31qo/sYIud4AE82wWUft73rHo++RIw1yC5HDlyWdSL+EvNqg9pGTi4DnkbBY6syEeK29wE8MeGjH02oO7FTGSJ3tQBPKx5P6oZ1DTyx4INx00bAA3i8wBMDPhg3bQQ8gKcUOrZ+x6pcgXHTRsADeJzBUwc+GDdtBDyAJxg8ofDBuGkj4AE8tcATAh+MmzYCHsBTeTvd57N9K1dg3LQR8ACevd0sn377Vq7AuGkj4AE8tcHjCh+MmzYCHsATFTwu8MG4aSPgATzRwVMFH4ybNgIewFN6WrlOvwEP/QY8NcAjLow+OLy/MiWC8i0+NyTw2OCDcdNGwFMBnl21CTN4fIvPDQ08Jvhg3LQR8Dh4PJssd/vgCSk+N0Tw6PDBuGkj4AkET2jxuZzBk3JZFHIoEeOmjYBHA09o8bmck72njsfE7i/goY2DAM+2XMryVCl1UiylclVR5qZe2Zi05W1itqWqjak/B0E6W97G5PHULT431KVWSs8Hj4c2Diq4vAse24PLZdUmcgJPU2dupM4UyeOZ1LRxsOAR4lptYsjgien5AB7a2Dvw2ArElYHHtdrE0METCz6Ahzb20uNJGesYOnhiwAfw0EbAA3iCBjmn5PFMasADeBoAT5MpLMp05pI8nkkNeADPgMATCh/AQxsBD+CpPchtJ49nUgMewDNA8PjCB/DQRsDTMfA0nR/ZRyfgoY2AB/C0MshtVK1gUgMewDNw8LjAB/DQRsADeJIMco5xKCY14AE8AeDp2jKm7UOOTGrA0yh4TMned7mYi/exXBO9A57w/jWRuoNJDXhaBY8p2fv64uj026vtz4cHn+QNdNdE74CnXh9TJo9nUgOeLDwePS3G4uLiWPVk1oC58W6ePz+buCZ6Bzz1+5kqeTyTGvBkCR6TVyTAs5hPnrpmH2wbPF0/I5MyeTyTGvB0Ajwy2VdVonfAE1dnquTxTGrAkz14xN+m40fvhJfjAp5cqkz05VTwkCtX0MaBgGdbZUKR5dnpavnrrvrEna+era4sFSZMFRdSVHDIpaJEU0LlCqT3VSb0JZbqzfgkem9zqeXz2V35Vh1i5QraOMCllggoq0ncxe8CQq6J3tsET99STsROHs+kBjytg8eU7F0AZT9OM7kWno1ronfAk0bfkCpX0MaeezypGgZ40ugbSuUK2gh4AE9mxj2EyhW0EfB0Bjx9zGccO3k8kxrwAB7AU0sf4KGNgAfwtGLcfS2ZQxsBD+DJ3LiH2m/aCHhaB8/Qv/mHEFSnjYAH8GRo3H2qXEEbAQ/g6ZBx96VyBW0EPICng+DpeuUK2gh4sgdP6Of11bir4MOkBjytg8eU7N2W1D3XZO+cZ/GDD5Ma8LQKHlOydyG2pO65JnsHPH7wYVIDntY9Hj0thp5nRyZ1nz+fneaa7B3w+MGHSQ14sgOPTO6uL69Ovp68zTHZe53PGopxd7FyBW0cGHhsuZWPxnd/zzHZO7e0/eHDpAY8gAfwNKavS5UrAM9AwLNN9m5L6n5WnezdVmUiZbJ3EqGTPB7pQbJ3W1J3PbhsSvbedHmbup7VUL9VU3g+eDx4PLXAI8SW1D23ZO+kAA3XmXvlCsDTY/CYkr2r8Rs9qXtuyd4BTz2dgAfwtObxpHTnAU/+hphryRzGBvBkCZ4YkwbjjgcfwAN4BgUejDuOztwgztgAnizBQ2G7+DpzOhPF2AAewDMg487l3htjA3iyA0+ucYm+GHcOSdUYG8CTLXgw7rTgabNyBWMDeLIDT65bwH0ybl/4AB7AA3gw7ig6feADeABPr8ETGoPAuMN0usIH8ACeQYAH425OZxuVKxgbwJMVeHK+X9Rn4266cgVjA3gAD8ZdCR/AA3hqgWeTxP3z642BjT7JdBk+pW0AT38NsanKFYzNgMAj4VIoYXMLGZ/SNqnBY/q7BKYtFasUmUdoV9pnP8WHK2RNkNafpaqjKodRVwyxicoVgGdA4NlMpNEHPRuhb2mbVsBzC5IyIEpgrvs1/fZK9FvmJFKB4AJZG6Svbp+lS22yLhti6soVgGdgSy0xMfRvaFvJmzLvomnwzKeT1/P55NLmoaz7cDv5FxcXx+I9st+qZ2erK6ZD1gbp5RZmdh3iGVd5Zl0wRMADeJLEeGzf+k2DpyqPs/RgNhN+9FFN41rW3q2np4DVB7ImSAudVTpEO4/Gs/dVcbIuGGKqkjmAZyDgUWV5Jif46Up8g199f3915+yl8p79ChMpq0xU6RTt27Rl064H3/9c1PHm2erBbV9M+sX/y/9x7etGXq5mt+1RP7Nah/g/pbJHTypXUM2BKhO1llrym1l+oy/mk6dtLrXKPB7Rlsfj43dyGaMumwrLLMMSbO2d3Hh40/Gjd/Jvvt6deEabNk2uRRuEziodLs+va9+AuVetwOPJGDzm2MTow5P52WVVaZu2wKMnrFch4AIeERsqe2/VUkuH9JXDUquP4FE9H8ADeLzAI+M7Mraz2SnaTGKf0jYpg8v6689nkx/UmI5pW90GHrEk0ie/ra6YDlkbpMXyqUpHX8ET0/MBPAMLLhc9CMsBwoozPE2BR18mFYK+ShtN8BAwEnEZ9XfVe6mCrA3SS8t2uqpD3xHrm3GTpA3weIMnJihSgscGwsLBwFsvR/cwBAj2l2+75ZlV9y1silvvRUgbDxBqoO7TrpZNJxVAAE/nwRPjqoRpuRXa78X57KktvuWisy/neKp05pQ8HvAAnlbAIz0d1fvw7bd+WjnkWfbl5LIPeHJIHg94AE9r4JGej5z4TQ9yX+5q+egMHTvAA3h6BR6Mu72SOW0mj2dsAE8wdABPd3W2nTyesQE8gGegxt1m8njGBvAAngEbd1vJ4xkbwBOkB/D0R2cbyeMZG8ADeDDuxpPHMzaAx9s4AU8/jRvwAB7Ag3G3orOpqhWMDeAJ0gF4+quziaoVjE2HwLO7BOlf5gbwYNx14MPYDBQ8mxvcO+BIcS1zUxcSuiECnv7rTJk8nrHpAHjUBGD7HpBbmRvAg3HXGXfGZmDgkUupk68nb6URyBQOPmlBY4CnKg4AePqpM8VYMzaZgkevyDBbvtxVTHCsNhGzyoT+f1QyGJYw3gOrMqF7NWoOY58KDHW+sUzfeHg8w+t37pUr8HgSgkeFS1NLLcCDccdOHs/YZA4eY0WE8ei92N1yrcAAeDDu2ODJsXIF4EkQXJZLKt3LcS1zUxc8TQQcAU83+h0LPoxNxuBZw0apn65vq7uWuQE8GHdMfTHgw9hkDp4YEmogNuMCPPS7LnwYG8ADeDDuIH05Va4APD0Djw+QAM/w+p1L5QrAA3gAz8D6nUPlCsDTE/CUGRLgod91bYKxATyAB+OOoq/NkjmAp0fgifXtBniG0++2SuYAHsDDBBx4v9somQN4egCeKsMBPPS7rg0xNoAH8GDcSfQ1WbkC8PQEPDHW8UxA+t1U5QrAkwg8mztbow++id4BD8bdtr4mKlcAnkTgETfR1YTvronefcHjAhXAQ7/rwoex6QB4RDqM6Xx+KT0en0TvgAfjzkVfysoVgCcyeARUHk4vXqtLLZ/sgyHgiQEnJiD9LrMdxiZz8Mynk9fCk1HB45Jv2ZbsHfBg3G3rG6r9ZA+erSxPt1Ujfvv15Wp2eH91+aa6wkSdKhOu76HqAFK3asVQbShrj0fdtdJF1NmqWmqFeDw+XhEeD/2O4fXkmjx+8EstNdZjCy6XJXr3ifEAHoy7yTbmnDwe8BjAI353TfTuCx7W6Bh3k23MNXk84LGAxzXRO+ABPLm3Mcfk8YAn0no6JkwAD/2OrRPwAB7Ag3G30sacqlYAngbB46MP8NDvFDpzqVoBeAAP4BlYv3OoWgF4GgCP70ADHvqdWmfbyeMBD+ABPAPtd5vJ4wFPQ+Dx1Qd46HcTOttKHg94AA8TcOD9biN5POABPExA+t148njAkxg8IRABPPS7DZ1NJo8HPA2AJ6YBMAHpd0qdTSWPBzyAhwlIvyvtD/BEBI9IcSofsinjoEuFCcADePrYxtTJ4wcLnnWOnem3V9ufDw8+ydQXPhUmyuASChDAQ79zAU+q5PGDBc/i4uJY9WTWgLnxbp4/P5v4VJgAPICnr23UU6gCngQxHllZYjGfPPWpMFEFnlhrbCYg/W5DZ+wUqoMGj0lEgvcH3//slOjdNdl7aLJtkr0jJI/vabL3grdzs5yajh+9E16OS2kb/ZvA9K1Q51sCj4d+56YzheezDXsoqYVDNnwKhRu+eraybQaZdFSlNU4KHllbS11y1V1qAR7A07c2pgCP+kUfuuGj/k2sWGybQTYd6uuNgUc0QIWKb4WJMvDU/XZhAtLv3NoYtWTO8rQAiZANH31+ivp4ps2gqrLkAj5lzkVU8AjvRiWd+F18uE+FCcADeIbWxhj2KVYSInZaNtldNnz0FYqIyZpWKFUrGQGmo/HsfdWZvdrgEUDZj9FMrgUBfSpMAB7AM8Q21rVRMdEfHJ6uylYS8ku/LO6q/80GnqrYrV5lppEYT13RB6DuoAAe+t2FNtax03UQuSQQ7LrhEws8LrHcToCnrj7AQ7+70MZQW60Cj+uGT6ylFuABPICnY20Msdcy8Phs+OwFl988W5k2g6o2jQAP4AE8HWyjr83aYjwhGz76drptM6hMR+djPDGgAXjodxfb6GO3pl2t0A2fwgHCs5erIkw+v5ZLrDIdje1qpQRPDH2Ah353sY1elSvEOR6HtDN127k4nz0t2z2T3lBj53gADxOQfsfX51O5wiXtTGg7pYdTdQ6vlZPLgIcJSL/j6/OpXKHHdZpsZ6t3tWKBJxYwAA/97kMb+1K5ohPgiaUP8NDvPrSxD5UrAA/GTb87Cp4uV65ICp7l4rv/mI5Hf98+qHvHH75bvPpPwMMEpN9xqlZ0tXJFMvCsg1uHB5+m88VT+Zq4EXvncPTJZYsN8AAe2ugPn9T9LpzvuT27s0s0tjkf1Bp45CEjU2R7c6CpuoGxs7MBHvrdxzbGBI9P3EhslwsnQpxKFjB6PD5+Fxs6/uBZE3DTqP3l1yYLWpXXExsUKcCTSidtjKOvK+2MqSdGBgeX5Zv0fMRhxcfT/3pX51pENPCUeTVl3hDgATyAp36f65aAcvWiXOdyJ8GDIEi7Yt88mh3JzaO6VyOCwCPhs5Xl6U2D768u3xhKZbx5tnpwuF/apqz8B4Ig7YrJgZBJxTbxnviBZSfwpAgud2HJwVKLpVZfl1o2HXowWY33xLyc6g0eGWA2bad/eTj66LOdDnhoI+DxH5sQ3a7PbePh7NJgqKk3YsMn6J/EAcKTewcf6hwgzHmQESRn8bX5HOdI1g8M8CBIP+2+8YfFACAItt8p8JhqRcvfbbWimxZ5kFI9/RnSNhnI3/SveGgzROemXaOPrnpcP8Ok11bTO7Tt8cen2F7b2NV+DpYxdNXpUhtdh0/bz7d34LHVipYP3lYr2m2C7xJX1xm4TTCuCImyOtY20bPByfK0si2+OncG7N42l88w6S2r6e2qtwwOdcbM9hxsY1fnOZSNofMzcKyNrsInxN56DZ66bqGtVrTUa6vzXCXq3ZQ6A7cxvuJxgqoa1K4wLCtREkOnrsfnM3S9tnESr7noLYNDjDEzVUgwjZ3v+Ol6bc97/nx26qLTtzb69gs4wDZ6D56Y+mTRMfnAbcXHqnRM5/NLaSChk1p+5snXk7eyPaYCaj5tE5NJ/q+acjJU597E8Cj8VvYZVaVOVF2uest01h0zm7ekj53vsza12TSGwePnUBu9zlwAPB7LGnWppUPAZSI+nF68Vg0m1Cik8YsJsXN/J9fn39y9KisF6xrjUZcqVeVlXcHjU+q2DnhUaLrqtemMMWY2T0QfOwGuus/BNIah4+daG12dD4AnMnjUY92h4JFlX1WDCZ7UmvFLgzsa3/09FDy7JUUxH0qXwKOOUwzwxBizKs9Pjl2s56CPYcj4+dZGl3MC8EQGj1orOsS9lBUXdYOJBR7Vfa+z1JLvU132Li211HHyWbrY4jAxxqzJ52Aaw7Klkou9u7RX3e1Sl2GDA0/MTuu1ovXgsr7mt8VjTPdXQkFhrC09Hr1/Mj+7LKtB7apPNeqqutahweWyAHbZZ9jAo49T1We6xGFijFnVc5Bj5/us3YL3ow++NhFaG10NNg/25HKsTptqRZu2033yiMSY1NvLdLffvOq3UlkN6qr4jhpQVpdb4Tr3v5FdamyXfYbNOzHV9HbVWxmwrjFmNqiZxq7OcygbQ2edNWujx7hgOnjw2GpF7x0g9Dy3oBtMyKTWA4kqJMpqUFd7PeIwW8UBQgedRV27XRvXGtu2zzDpLavp7arXBzw+Y2Z7Draxq/McysbQRWeU2uiAJ12H6z7Q0sNomR6+6rPYJjFjFjYvBgue1B3mrhaCAJ5GvR3AgyD+AAI8gAdBGocQ4AE8CDJI6TxhAQ+CAJ5GvR3AgyCAB/AgCAJ4EAQBPNFhk/tZBQRBGgZPU0FlwIMgacUl97Nvzu6kMGgDPBgKgsQTn9zPPjm7O+2FAB4EMXsosZJ/+eZ+ds3Z3SvwYHRIX6V463z06Xxx8afNjfr9pPj7SdOKN+93F3H3E9y7QK0qoZlLArXOL38ADzIkUbNRzqejX2wJ8feThxXLBT2fTX748t7BR9ucLUvX4ZL7uSorZOe9EKCDDNXzUSfyLrezGSIqDISOx9NHP/kW+/PN/dwaeJoaDMCDDEnkUsma3tUQ49Erc8hMhj4ej2/u58aWWnggCJJWpNchYiy2GI0tuLzOanjv+MPJePI339hOaO5n03uTgQcDQZA00FF3h9R4jwt49DzQzp9bM/ezKR0tA4ogHRA9tqOmiC2rF6+LCCrbclnbPJ26uZ9NyzYGFUEGBK8n55uKqW0LA4IgQ1mqRTxYmDV41DrUTT1Y3zslCNJ3kbtXOVXgSN7hpiZ66J0SBEF6BJ6mC8aH3CnBABCkZ+AJmeA+91Fcll1Vd0owAATpEHj0MqnF+tCb7bbvXn33xZPZ4s91l2jyPorvKUuXOyUYAIJ0zOORh5H0SW+7uBYKthBAuN4pwQAQpINLLX3XSp3wdRum30fx8Xhc75RgAAjSQfBIr2eb+yPSOQGX+yhlMHS9U4IBIEgHwSMnuvAoXrx68dnj8fG7uhPa9T6K8X8D7pQgCNJB8EivZ/rNo5/kOZpQqXMfJfROCYIgHQSP9EpCtrwRBAE8wSI8k6Px7D1XERAEaRQ80/NFFrdeEQQZCHgW57On7BIhCNIYeERw+eH04jUPE0GQ5ODZ7SI1l/YCQRA8HgRBEMCDIEg35F8d3N7ZhHOb1AAAAABJRU5ErkJggg==)
The coordinates of the corner points A(20,80),B(40,160) and C(20,180).
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAjQAAABlCAIAAADVpO4vAAAAAXNSR0IArs4c6QAAJAdJREFUeF7tnd3rXUfVx58+9yYacxVCCGovQiqWVA0UW0ghrTYgDVo1VKTQYKuCINLGl5ZepKlRWoRSUw0tBGmrsYoi8TXQXqhBGxsUGnLRKBJKrtQ2+Qf08/h9WFnOzN579j77nLNPfmtfHM7ZZ2bNmu+aWWte1qy55l//+tf/xBMIBAKBQCAQCEwJgf+dEjPBSyAQCAQCgUAg8H8IhHGKdhAIBAKBQCAwOQSusWW9a665ZnLcBUOBQCAQCAQCawmBKybJG6fYf1rpNsDwIiS40hIM5gOBNY6AV2KxrLfGG0NUPxAIBAKBKSIQxmmKUgmeAoFAIBBY4wiEcVrjDSCqHwgEAoHAFBEI4zRFqQRPgUAgEAiscQTCOK3xBhDV/y8EvvGNb7Al+9vf/naFcJkOz9///vff9a53ASAP31cIw2B1ggj0ME7/+Mc/vvOd73zwgx9U4+PhO2/++te/TrBi82NJda+nPx3dERKsl5pSqrWvlq3qW8ex0oPSvn37/vKXv4jghQsXcsrqC03P6DjT4CmLQot15L2Z0k984hN//vOfk2S84b24JWVOB/qf/exnN2zYQAI++c6bsfCchQ46+atf/aqvnadWw/bPf/7z973vfao7X/g5Cz8D8+J8rIf89j3/8qc//emd73xnUxktGa++vwRCfb2+/vWvk/43v/lNfZZhKUOCw3DzuRJh3XbbbYuR3SycL6yBtTP5mc98phMrsdr0jNtHUFkf//jHKYtCc87FrX/e9ra3YVktJdl5k6T5yle+Ygn+/ve/v/e9700S8GYWUY6S92c/+1nCOc24F9vf+973chlBdhT22ol4JXZFybaoNsQgywT0nkUaE9LirwUwvbpFLEx3hARnbyQLE9bsrBqFifCMBhymmqUKsRYjYuJ1a26cMDwkQIPLHKLfZKs8DzJsvOFf0pBSGt8M2Le//W2pRL3hU7aK6oxVEQrttPdJWbAhPtHMVDPnpIZtUSClsivLYvR8b+Mk5rz5bUIf02WjicSSkUVEgM+GLaAvAdCALC/QWJuwgkim5qIG4VuAUeCLhrpNatpSkl18FsuqqYUxpkrZMI2f8GnNwvix3qKuQovni01GSTZ7m24xTouRYI6/ZK22TmWpsrq6Hv8vacDNxs5SuAjCUFL2pOF5DD3s0iY17crLGgrJVEk/rVD9lC5TpfJGzr/oBV/l9r5jNH3V4MprBxizpiKgvN5JjFPRVuU8tHSoAb3bmre+1OgKlSLLBIy+Ycyu3D0/xWZDgqTHASyP79eJOlYnMpUtwSWTLXV/Ecmn3ZpsUUplZQcYJ6lWYzJHspNtFZqMFaR71erUwBL0qJF06Yyy892tauaU16fIQXEy6OsgDeWnnGac2mfQRcomAKGZTLGLHCplXpa1J+stSWdLauH7XpGgDSGbjFP+vsW0VMq7hcICJJjjX1wYMajVmpuUmjpAnsD3uuLKjGntJln7lZliu6Jcs5FF45Rw5ZeDiks97cpaPCTaRLrAVFiCkpAxtTjAOLV3qAG9e5hxUgsZ3TIZ/zZASWpU7A7+ZVFBJy+lzRLK/qVauDdFarHFCU2Lvuq12lnkyhPvZLtoe/xLbSsm4w9Z7l6sFqvc2zh1VlijYPUZW/ejAySyUQsujnB5T/3V3zSDtlGMydgoI10NQFQ9NRpPoUmbm8ICSitLWlUtprIWiXHylbLZvTXBfCSrVQVwkPbhk6rVDzabaufl2tJnmrJX1r1Ggn7kCNSqps2YhYxas41q+ZcGYyMvgaYpsrJbcxJxG3GLmmaivs/kraKpXdnIAx5kFdqNk82WbDnITIt4gIhalySb9+REBFLQ9pJcZGkZhKqUpNBk0pmoCc9DZ4fKW0hN20gMeVMzs/eyTN7K2l8mO/Xr/KlUgu3GKeHQ99OmjB7GolgTEERHXbs4CmlHqe/MSelpfjazz3trJ9vFmXcCiLqJnzVip0dZ9/NKrGrm1Nm7TNckcz1GqeQ1oyJ1k8ij2A5Uea+Gku049Xm1UVHwI+J245RM80VKL6UxO2uRGKf2QUQubHV1W63u7MaVCbxcc+PUafwq694kwQR/1TF5KbUrqG2nobjEUewhak4Set49eKlxhm0SWFmGRt6ukilLUm5x5uSx1TjDWpS6aFKjzu6jetloJh+EQhC4bNVRytoK7TtzEvItHSpvbzVto5dxsgWu4jTiqjFOICnpyFr0XfUaZpzUPJLHzHmxNXrZ1Rgn6Uzr3ckqdKW+KibzSqzWlfz8+fPFOtvLS5cu8X3z5s0+2Yc+9CF+vvrqq/by7W9/ezsd/btjxw5LJp/UPXv2eA9UfiZ01q9fX0M5T7Nu3bq+tWgvaPv27e0J3vGOd9BM//jHP6LIcNPEA5VDIfN2Qp23BBP8L168CAiPPvqol9rGjRsNmd27d2NLnnrqKV7isY3na6e7qi/izTffhBRIeqjvvPNOfp47d64J/7xddQqrXZTvec97fAJMMv67lY3cMt5zzz1851SG3jz99NM0jA984AP6iVvwzp078dI+fvz4r371q2GN3Oeq7FA+S2XvruSNpo7Eaf/PPvtsAqAoUPd2BWfgVJa4xGQPPPAAqp92jkwPHjzYyYnvLzfddBPp+fQvOx3uKc5Mvi1XPPnkk51F1ye4/fbbqQ6VktZ64okn+PzoRz9aT6EmZZVxorZUcoLnmU6dOlVTyQmmOXLkCGMZhh4oMmSM6qG7zs8+TUqCL774IhKh4qdPn9ZSHhXHjDHgwE5PUFjzZgkTi4B0apWzNWjt+++/3wp97LHHtN7I+FRKp3NiMZjhxXSohx56iDoienTcYFZnz5h0NzXLTZs2GWWZZHtkFfx4KO+wjB6ajty88cYbs/NcQ+GWW24xkw+3qBpyMbKxvDVsX7582ZelhrFlyxZ7+elPf5oanTx5ErtArenFfcdknXWpMk579+6FULvi0Kj29ddf90X+4he/4Od1113XyUdLAlEuetkzKpmFsvKKZ+E+v1rkfDL6O3To0C9/+UvUDVaK7toy5J+xmouX4Fve8hZ4Lq61UmWrDocc6TxYKdZ5NMBsqenf/vY3/pX6eOtb38pnMmB64YUXeLlt27YauCTrpBPWZGxPM2yEcffdd9PVsU8/+MEPoO8Hoaojf6HKi/OMvjwP6FAj9gvUCFKmYSD6Js4xAy1ndWc/Fo36pmgUq2fg5ZdfZuVNtkczM6/Q+Xn27Fk+TQQ0V/qsb4E6xpt4BnF0F92tDfW77rqrU1h+ylhc1muZNarly8omj3cMbmf7xhtvJO+JEyc8hTNnziQ9S0308ccff+aZZ/hy7733dlatdwLDgpxNU+mWc04sRmsfLN8y1Tq1d1bhZ77zUdxz0rqn+BFlSsE+eQ8CbLXfc8odRvPq2IahbeUlXhsDapFXKmlSqotnjwQw76tTXOftu3Q7KQnCvDwzzfdEQ360krZ5+OS7LYWbM4JqbaCZxBN/h9whQq5Q1sA625W2i2BSPGhfR5547Q4R+X6eCVd7WuYDQhEJVy1djKLJnu9MJB7JNJvkbGnSeLQBYO428rXxyHR2qJzJmn5Rs+dkG43tbbtzajijQ8TCzjn57fBcD3R28L57ThC041lScbasZ9tdI55zUlmJO09npdoTeCVW5RABuaJbsFlClVfjSj7AODVRNiXS5FrTZJxyA+49IPrWotM4JT2NNlrse7M71LYYp8VLsKVEqXL11eRJvPWSf+kGfv+8xpU8GbL4QY/1ZF/KjMZJWi8n2OmNAjP+8J9vujI2Oc0mh4jcR1+V8jx0+tDnfaezX9QYp1zi/k2lyalRf8WCfMYFRIjAMCSKOxlndFZkgHFSoUn1vW4pnnZIvJyKss7XrqxlJh5knfVqSTDEOGloSX8Qvnr4boNEldfr+KqydI5wLZnGlSqa74ZIX+NEXtl8nvwQZd9aJN3eauR7GrhpWg3/8o0GN0OSv/JDxwME7OVazL5ICYoBDdxsSQG0vWc5Myd/ZNsbElkRnyA5gSD6BqyahDddNe0KQOzArNzW+3rrwQNFJ9Niq5RYShI0SdZmckXDIAx1Etn7lwoE/vLtDVJqXZqHFQ+mkL6pQzVx2N67V8s4tTceIQCMpiiKZ8B1lkBKSVB7R00dd/H+1vnJp/ZuPsA4WacTV/nJdxK0sy2W2mVtbGt1pOhwO0CDqTdZxtqZ07CSppar3oxNjfMafjqNUw2RiaQZZZ1zCnWpN05T4DZ4mBQCw4zTwqqgQU9f//h29rwSq3KIsKlSfAkEAoF6BNgh379/v+bW9bkiZSAgBORSP1m/+R/+8IcwORdXiP9UP4xTdIRAYEwEvJvZ9ddfj2cUlmkUL7sxuQxagcDMCBw+fHiubTuM08wiCgKBgEOA7mo7o1rx967zAVUgcHUgwNkGDj9wBGJ+1blGe1A8vS7Qmx9DQTkQCAQCgUBgzSJwxSR542Tf1ywuK11xhhchwZWWYDAfCKxxBLwSi2W9Nd4YovqBQCAQCEwRgTBOU5RK8BQIBAKBwBpHIIzTGm8AUf1AIBAIBKaIQBinKUoleAoEAoFAYI0jML5xUkRhrikaFp55wfLAIRJuWwIkL5ifKC4QCAQCgUAABPoZJ06864whceCL8GGQ8HzneAdnO+x6D3IRJ59L2JQXu1XMzktLg7VQ/Pn2h+K4pM5ycSVSfmEddKCmokmZFM1fRHsjNr5d9dZV5mr/jzE2NAAkARn0PFZILR9hdIqpHXDggyaUN2zYAAN8FktZbZSD+0AgEJgdgStR9pqvzLA0uk+65br4Yki0YuyW5KafziDBeUSmYnhd2PMhcovB1PNLhnRwcsTwhQsLb+ULou4t5VI7i2JpzcZHCy2GIk5ipXeKqRPwmqDIS0EvCg0EAoGlI+CVWL/Ar5gltJVMlI8ArSop5m5+OwAajdmJpdeFIjxmDGquV8lREx3d8arS7QYpS2y3m6gsdLFO7/tQwXrPy5oboZYuvBYG2o2TDSzsHqmElJAx045QFF1b1y/x1IipE/Ca62SmDHLwFggEAvNDYKBxUqB+mRm+5MFopXeKV9YmlUnuNdF8K7kUBF3J04JCyyzNcmme54mISVO49heKOEk5PwHMiXKLcbL75Vpmh7L0nrfEZteIqRNwid4PDtScsGpzgiXIBgKBwKog4JVYjz0nXdzL7bxEsUSVs3thq0P68tJLL2FOuEw6ed/006Lt6l7h97///T4lP4ndlNzD7RPoOuHnn3/e9kX4wl3LtvSEawYJbr31Vp9r+/bt/Mw3tO688040Zs1GV2XtJpVM8YMfeeQR2wjM2cNsgJ5A03Pq1ClJXD87xVQDOFdWMwjQZdh6FBSVAKmTQiyYCQQCgeUiUGuc0PtYI4a30m5cBIDlSLwPfv3rXyeWoFg3DAAaKt+98AqLjLfccgufFy9ebAII28ZkC642btzIpjoeDThEYNIOHjzos2zdutX/lEXMbZ5M3blz55YrjzmVLrty6dIlvFGafEOee+450LvpppvkNsJD1GEQTuTSKaZOwKGfVFNrs3Oqe5ANBAKBVUSg1jidPHkSa3THHXeokrt37+bzu9/9rq8zCXbs2NGOAkYOw8bEKzEhw7Bbt24d7l7spmBs7rvvPhScTNqAZ9u2beS6cOHCgLyrkgWIbIICVgcOHMCce+YxPIiGEcbRo0f5F1u1efPmVald8BkIBAJXEwK1xunYsWMs2ckm8aDFGO3igd3rMBNzpp07d5LdO5oPRpN52549e2Ds0KFDEGQ35Utf+hKD/UThVtJvWe+qpDD9ZLohXqvPbA0iUKawtpIJbtj406dPHzly5Pz589pwYiKVe+dPv6bBYSAQCKw6AlXGCZ2FFmNixAKa3aXGGyrPjKoSAjYkdu3ahUJsskyJndNK1KZNm5roP/zwwwzzbeMK6/LAAw+wWsjkwG+csJblKeivZG2qsgqrnowzTGaD2RrEllMjyRELBG6f//znrY4Ay0IfP5944glf8U4xdQKeD2i0EbXq8Ab/gUAgMCICVcapxQI9/vjjNdywgcEYHOXIwDyfo2gtLimFzXksWYsVQZmyNtUydZPdYnrnOTx79iw/85tJe00Ba6o8qTQ33HAD/Hibbext2bKF76+++qp9NnHeKaYawJlwIzi/56epm9zW4wkEAoFA4P8R8F7XTe6GjGqLXt061GJuwaQpOgTLezjxFPdl1RygIb30l9FR6RDXCSoWrPgrOcbUeezG2NAqVguT0/fFhP8mJg1hc/TXsp6JzxLgZK+lP94YeiJbI6ZOwOOc0/QbUnAYCCwLAa/Eug/hSiXlURW0b+H/QjEVbVjTQMCfqukMPYDGhI6nXwxGQBp/hqkzYIHJQId48pPFyxLSgHJbjBPUdAg3ebwxzkVAYsYl/mhUp5g6AY8IEQMkG1kCgTWCQD/j1BQPQmBhLezsatMh3BrjBCnMg208YOcSO5EYQpXOpA11qRkAD7nyI8A2A5CqbQoDcXUfwhVcmCJbPQMrH7soTwBWiD4/tNsuJj/lagIcmiY1ZMf3VQ8ctUYUR1QzEJg3At44XbnYe/ZLvtm2ufbaa/E/xuVh9GVTArw++uijWKN5+DKwGcOWGGoXl4rROV8YwdkluDBWo6BAIBAIBHIE5nVNO54OOIDheVXceJ9REpzwZbA/D8sEY4ROYAh/zz33zMhkZA8EAoFAIBAYBYEqb736ktDvLAdxa8a4zm9Qw8XrU5/6VD0n9SkJLYFB/drXvrYWjjrVwxIpA4FAIBBYIgL/tay3RD6i6EAgEAgEAoFAgG0tgTDmnlPAulwEYs9pufhH6YFAIDAjAvPac5qRrcgeCAQCgUAgEAgIgZH3nALWQCAQCAQCgUBgdgTCOM2OYVAIBAKBQCAQGBmBME4jAxrkAoFAIBAIBGZHYHzjxCEnNrW41G5cb/LZqzqMArXQBX1X6yW5w2CJXIFAIBAIzBWBKuMke5M8hBjPb/pBlXPIiaNOLfdiSNfnB3WJXM4dqSoF4r2MAfEjyNWEFDGwSeCJJylbiubwE3WhRh/5yEeuDnPbhJVQ8lflcr9wscrcPoyArD0kkuKn/atLdRO0oQllbomEAp/FUmhaxglfFnmnFPdawVh+XS+10F8tLa1vX1XPGnYDWd+yIn0gsGIIWKwk+G6Km6SI3cUnic+m8Kl50DZR9kE/kzSdEUWbePPByItpLPy28e8DzpKlpmgh0BSXb97xpirpt0jQ8LfA7TlNBY9PHmLx+ZSgrbjj/vGiHCXwK0zmnORREyth6ZvMcEhC1KsNKJBjX5rtPStpkGMRDzqBwMoh4DtXd1RyqperZkVcTfQ1mouu29LTFLZcGRONpm6vlwoMyhs+28GVLbQnTwyf0ibEMC1GHK+5BkJkqRekphyitF1pdmKFdEhjKPFFUWK9pBQFmHkkpqIIxShXZkhkFl1eAYUtvvC8+5uME59JibzRM6Jxmnddgn4gsFoIjGCczGL5+ymaopILHQWiRuXlsyu9SQaqJC5ewOGx7lS4MnKeyURU9UUrLPqUL3ya0TjljTiRFJZeRqLFQudWRK3CRCDlbneAUajGB3YTmEZCybhENm8xF5qIw+R+L/3kMzFOtAo/48Sc++m1AEwm3H5wlgz7lB6aDAIUoZ9PQecjyidx3GVK835ho4phZFdLqQW3VwcCIxgnlAv9ga7o9VTTfU6g5u/dyI1TrrA0U0m0WAv6TePZzhF3r6K9Dp1gU6gc0VeO/bUc6pf1iobc41C0K8nLokT8y2IpnUWPKA7Dx0+eaNsyAAl6yfCIivD4y8/M1IlDrViaqS4aJxHxT36HvTfelcapL9kRIQ1SgUAlAl6JVTlEqFkfOHDA9sDpLQRL/eIXv+iDpRI4/NZbb837APvn3HZBt8wvR/eJk4jjuhT84sWLOcHKN/K5QL3a9nuTq0Vl0Sga4s9Wlr66ySTlT37yk8SY97efvPjii1Tq0qVL3mki93fYunWrr7vubvf3sue+BgCraZk9mzdv9j9vvPFGfl64cGEWVInw28vL5sEHH4QrWi/MHz9+nJ956dyx4nsd6ekaTz31lKV87rnnsPEf/vCHcQOhdJoidu7ee+9tqQjp6Swa9sn4QRaDp+km9owEcNUXijmR7ctGpA8EKhHoYZxyivv27fOORm+88caOHTuSZPQiktHZ8OCq5GncZKgVlAW8iSw/r7/++mGXetxwww2JDh2X1UlRA7GjR4/+4Q9/SLi67777zEKDBkOWVXE22717965du+rtE2YVq4lNeuyxx/giK5s/EMTLERAwulgmMLHGRmJGbz/96U95c9ddd+3fv58E3/rWt9oFTXo6i4Z9usYFE3Xo0CENoWCDK9N8EZXNZk5kK0uPZIFAXwR6GKdk6Vwb5syf2gdxx44dgyfsk826UGe84XK/EV1yW6qNWrG9CvPjePLJJ/siRfr169cPyLVyWTQVkN/dnj17EkNug3rSaOmPNlCv8ZeIBsqdi1GwT/WO6Zo8MbgpTpuoCxNHxjosDABC08AFc0LfUYKnn366180sSqw564jPnMiOyGGQCgR6GKcELNbovvnNb/LyJz/5ySg4Jkdq1CE3bdo0I3GWB205EfV05MgRCDJ/8mTnVPSMnC83u8n31KlTnhMb1PPy9ttvZ+mPL2heS8O6n08v2+YXTvOzU2RPtlUuX77siYiHLVu2NGGSn8MrvmHax5wDi1tpnzR5apo2sdzHSAvzzB4Sq21aiPP+EQm3A6Y7y20DUXogsEQEhhunSqbZtCg6yMmVSES0vXTy5ElP8+WXX6bbz3L17bZt2yBYHHWaKuxVdKJ2KxFY3WSvv/66Z55VTX4WV0RlNrTwlRj+s2fP8tLGB9q381tQmnXJbZ1H20snTpzwRZ85c4afEmjxqdxuZQajEwuY1Uq50ID9xpvPpQ1RzDN7SNS9aUoEYtgwNo0omnnb1XGUuxK9SBYIDEZguHFi7PmFL3yBgu+44w4VT9+TEun7aLDJXrEUnyIIMMxMtqm0D1+/FYyyYPOZUTnUpA355DtfzHGjsmjV6JVXXsn9pvpWdrLpgVeb/+IQ+QorWQuej33sY3yyt2/TDr4cPnyYl+yCKA2As3hlQR8Q6Je//GXes9+jBHv37lUykwg7MbyxVoSWpyGxkob/grLwBYMH8u0ONZ3AYgVfeOGF1157rWn3qJNCMQFtXvaGGsEqgyqfjL9ADNPLppFtPg0rqCmXVtfVd+CBlUYJJZ5AYLURsCEn1WgafrZEiLDjKeRtcSX3lItRJDrDNLBmAofJyaeiI6/fG7NDuF5IiQd8Z9EeIl/fytH6wpK1SND8vpLG6rEqtuPkvJGOBCSPP/s15QgRVNafr2qSS7urffKvTfgMkySEBAl4Y+UmJ5+KruRJ8BQoJ8eYOt3ZxUNyzqkv2YW12ygoECiaoeEzJ3oIWsnPY1iyYLpTuZqfKDi2gui3Ni/BBrz00kt+TU9uY7khaR8aQIFFJJ3/JSX0KSWJ+9dZtIpQvWyAv9pDkhL3eDcAlIkArYp8tUVnD8N/fxoUMaHy/ASXyQ2CsxBHApxcRkGxCk0iihiSrJtBEGZM7/OFn/ULcU2iwe17llXiIlk4t8oKDZtEkh4vPprfs88+a+XCAx2HVb5h/qJFHqCp5Ur+ldS0ERhPILDSCIx5TTsrGNdeey2ds2mNfhak6Of4RDECHV2/VHKFrzArNiwK9fK2qiQ+SjJ/w/EoBINIIBAIBAKLRMArseEzp5xjtDZDNlv+HrdKnPBlZLosy8Q4l3pRu8lapnHRDmqBQCAQCCwXgTFnTtSEydPOnTv5wirciHocshs3bhxlbWcA3HOq1ABO2rPEzGl0SINgIBAILBIBr8RGNk5Ug0kGB2xZ+2660mmRVZ29LCwTC3rsHLDVP6O32OzMhHGaN4ZBPxAIBJaIQKNxWiJPUXQgEAgEAoFAIGDnX8efOQW4y0IglvWWhXyUGwgEAqMgMC+HiFGYCyKBQCAQCAQCgcCY3nqBZiAQCAQCgUAgMAoCYZxGgTGIBAKBQCAQCIyJQBinMdEMWoFAIBAIBAKjIDC+ccL3esN/npW446cGRMKYsk1ncUhrskSaQCAQCAQCgVkQ6GGcsDooaA792E05fOeNv/4AVj73uc8RYY8Aa3YqSJGS/d3eFrXas07wOkvDl14x+kgMV8V4ZbobG2NJAj6J25ZbzfaiiS9HcAquAro6zC2BoIrXPAoornOVfBFBfgU7bYDsloYGkIsJOoAsIqQsEvESGb0xzNIfIm8gEAhMBYGaqOS6F7XltggjkkRZ1vti7HBO6fpYvESrzBEhJERNvF4LEprEXbbrXBPKhMi0u3FJU1M0MdHJlQSHruFtkWmoZntx1ILKJmGzLUvxljzCkFsCsudBuCl0VaKSL1IWUVYgEAgMQMArsSvqrEW1oZVkmRQf2psilBd/eQWH7tOVoPZwTyjJzHLwRfrRk9IbUioXX/jpKRfrmdzlkRsnRYymdLFk17T7my8qiy7e9DEA/fllaTdOyRAhZ4Po4MBuZlsi4DFp6g02TBdA8F5v/D0mAhxSymWytjsjlIWGpDd8yuB5C1cpkfkhGZQDgUBgKQj0Nk6mldrZRa/JEnTWqnirTXJ1kNScn+LkZDuNU/FuHmlYUROFmqJ1oVSSsrOmi0wwo3HKWRV67dcCJQjnQwo1Hht2KL2/V0nNxoYL9RJZJLZRViAQCCwAAa/EqvacfvzjH5MnudpHw2r//P73v+en7kuteeyK1VOnTpH+5ptv9rl27NjBz3PnzrWQ4kpT4VVcOSSjbmH3vgzal7r77rtFtr5o4tiiWOvv4a1BYJFpuPVHWBWX79pB1r+S1/PPP28XjfOFa0Tski1ha7cMK9f27dv5tO06grszIfbR5bU3SfTCvhJZJHpRViAQCCwYgSrjlCuUIpc4QbAg0xkdFY129OhRNFRyW/bmzZs9WanCCxcuzIIIGpmZHL4MuEKwk4+V4s5s3iQXwFcWjanD1yNxAJmFvSnnxZwgd3+7I/LS9ZJEiMeLQd4xXN918OBBX5GtW7f6n5KyBw0viaTiWir0LyslMmUAg7dAIBCYBYEq40QBuULJS33zzTf9NaBNbD300EP//Oc/f/SjH83Cd33e9evXYwhRstwIJSv17ne/uz67T3ndddfx8+LFi8Oyr1AuBhD79+9nNygxPOvWrQNArDvGBjCxKJqbxhMIBAKBwLgI1Bqn8+fPz16wrp9g6O0dzWcn20KB2dLhw4e5XIqbwk+fPo0yZdFp3759vB9QLqp5QK6Vy8KcSZdyJZee4DW+Z8+eY8eOASZ/sQnH7YvAi0xXro7BcCAQCEwcgSrjpFWXGZezyK6bzpss0+XLlz1Y2g3asmXLYASxhdzszpzJrj1kq4OdMyYEvPdkRy96MM9Lz8i+0a5du1ieza/jevjhh4HOFmNBlVVT4GW7yJ8wu3Tpkq+F/vKbTLZlZcm0bhwSWbr0g4FAYDoIVBmnvXv3wjHbDIP5ZtAtj+HXXnst35TS9tKJEyc8/TNnzvBz27ZtgwuVM8Urr7zSQqFX0YkNG8zYZDNyYJaLItmQY5aZX2SMEWKMkpsWq47s1vHjx30Fz549y08TOgMd6PiBjnwl7ARVL4lMFslgLBAIBGZFwLwDIdTkKdhyzgkXYTuNhDewP/Ji1ORK1+6EXXO0ha2OJjpNh5BElox2qkYp/QmqmqK9T6B3g16Ab2V9ES0S9ESK7vXmxefPGyVFy7mf7PLv90d6DZM451Qvr0gZCAQCCQJeiVUdwiU/+khKvPioAJ1oyU8mtfguG2c1YRo0uPb0k3NO4s3HcSiSpSL+uG5N0eaEXbS+E2lh7cap6G3PSz86KQrX8GxqA3aGqamddIaZGDFcyERkEWwEAoHAAASGGCeNlNFl3tLwHcVkEQSaDuHWGCfoWxQiLfIksYt0BjbRYp3GCbKk0XCeB9PCBC43n+1FC+Kr7BCuAOllnABBITZsmAKweYgp4DXAmaH6IgxJIyKJJCFFOhvDgEYfWQKBQGD6CHjjNPI17XJ5YGMp37FomnVVvperGLOc5IhSZfbZk7Efc+DAAUxdcjxrdspjUYhr2sdCMugEAoHAUhCY4zXtDz74IMdUn3nmmdEr9rvf/Y5R9rIsE14A+EwzBZysZRod8CAYCAQCgcASEajy1qvnD93Nkg4zjNFvl+AIrY9WUM/SKCl1D0hTkKRRiggigUAgEAgEAobAfy3rBS6BQCAQCAQCgcASEWBjTKVfMU5L5CaKDgQCgUAgEAgEPAIjL+sFuIFAIBAIBAKBwOwIhHGaHcOgEAgEAoFAIDAyAv8GYa0dBmMuqKAAAAAASUVORK5CYII=)
Now, we find the maximum value of Z. According to table the maximum value of Z = 136000 at point B (40,160).
Hence, 40 and 160 be the number of tickets of executive class and economy class respectively to get the maximum profit.
Question 6.Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively. They supply to 3 ration shops, D, E and F whose requirements are 60, 50 and 40 quintals respectively. The cost of transportation per quintal from the godowns to the shops are given in the following table:
![](data:image/png;base64,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)
How should the supplies be transported in order that the transportation cost is minimum? What is the minimum cost?
Answer:let x and y quintal of grain supplied by A to shop d and E respectively. Then 100 - x - y will be supplied to shop F. Obviously x ≥ 0, y ≥ 0.
Since requirement at shop D is 60 quintal but supplied x quintal hence, 60 - x is sent form B to D.
Similarly requirement at shop E is 50 quintal but supplied y quintal hence, 50 - y is sent form B to E.
Similarly requirement at shop E is 40 quintal but supplied 100 - x - y quintal hence, 40 - (100 - x - y) i.e. x + y - 60 is sent form B to E.
Diagrammatically it can be explained as:
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CRAremQ4F38CvSL9cbdzRswwCCkAJkZS4ic/AuKCLDTOT9zuisPgVtwapNIvHVFDiJ/RJxw7oZ+gsVYTSgmXFuU2GlatAObebPbWqPgiwVzKJXQFh3U4XMTJ83J9/hjR2SejTg2wwwuQct3r71Zi4ZmK52cO/hCcjBqE3TaxFApDKTI/iHHK0EfBloAEI8Ci/NAusYKrC2YobfGXjPUaLm5KZGzGiWzbihn6KxSIqzSVHdzHMcUQGBOY7vjg1WK3U54I6IRkmERz8WhEGkDkSlgLFvJsJ5Vx/8AaQk3DhPoDWHBKgVj2q0jkCQaSBVIFuKPg0zjEQTIQ+r0obiIQHoVPwL+tjkIRpTT4DYJM4uDCxzQ2xUKq5utM3RRFiABAEcU2kkDG8wiwHaXhpJl0BQnoHTgqN8CoyF24UNYc0lxf6ibaOuH1phjLkEEssMmtPNJfByG4CRwIlIO0UXnCSWAg9AD4RsBaxErM0fRaBYbiIAyeH3vRukAlYSAc0JgSjGyAWS6JfNHKxNAQQdkoqUVrYIkVnq9NIh0JNGGebKWXgNttCG9vw0Dtf7dBgrZKvxiDkKPsq/mi1BCR9g+g6sQSMc1CICQYuwUbbZhy+LpTC2HIwyTA4NetIPXJkliTeG0dRQ5od7V4PD2y0s/kaSP1Zl8xUK5d5dwRYT2cU7MSCGMIYLfOclLvRmfFbqG2FtTPi1TQdgBLcQq6CiAIt6UIFnkh9zVBIEiGKziaFQdZYCXmiPRB2ZBCXZfFSN8ZYJLVmLV9N5963hEkbHBQiADdiKVcB6wMtJsSWKJARcOzxQR9FpnEsBICrRwzqaFwVRhKviAIhTKbhq9qLlCkuI5mczLM5q7GJstmQkibREVC72oVSBcnYH0pQVgjQxgbPhRcCSzCJATYXRFTCIKjISIOLq+1MC2ZBYfCp9CMAz5cEx1M0dA9AuFSSY9sxWajt+C9hn3bpj3qO6juo7phQCqQBytc/A5AsTEbdTUHFGBcdgNkp4yEmtz1mjr1qyZJiy8Gn5jNqqIBytSqFAof+OVc/lch25ky+NHR9JxQqdvKsksHI39+qJHgi2gtD8iiPktSEyIhSMBt/7RhUdmUbfIZf8A2j6Dip4GgiyDqRVpSmADhb+TVHyTTsANrahpYX5XktizLhoeUga7HDpePNQU0Z0YLI03myhGwGWB0380GLgrG8u5jU1g5AzPoNf7h+6CBEgST3qNgVBp+FSfYanEIKSvN85Z/wAU1ohwJyGTvFBhjJlJYgb4j6aU9wUSCLIf4KX3LVtXyzY5uZ7oXzBFMRey+Gv9w/dHX9BBIFiSRqULg6lvcPBaDzTDIZDwAWLzm3rWvsAB9LSr4cyELkLybNmKZ6SKhSTEYul+axtqo6ZxMvNCEASbk+00PUGMz2k0sdGLJGYyy/ajQkIEjmT4ZgvUwBQT4RwdFBHygQnAEfE4y0/AILBcgyfCqKNVkBDqwoQBMgg+qXXNJgFIr1NdD7HkBgX2d80rS2Gk8z317TQ/TiaZ5kDT0aLagkW1jFtEUNpxmCgTwh4tndTQWOlgwErETAgEHOTlzUfUM4koQtxELO23ltSEJ8KAMLNEM91fUysmnKsJ9aQMUswQFNXKIhHnNBYJFlKMTk+9RefqtPqjyQ1czDeGlAZajjhe/wA5ourCEicjUz9M07hZrjCJcptxGIWCIp3LVdwllu3y/UF+spAFSHwLg9g/Xu6oQuVr85b/AFTFiJ2C+2m1Fj+CwGhQy96NgUokTzRy9hJBTu9SZHvgJx/2tnDTK4TI9NHzrTRIEi415tQtRE+hxdH3r/V8fOmpqfhqoMQOevAfvBRKszKjp39cuoKs1bKDgP4l3TYZjBZIbe1TFeQyTJEYmuFjdIooYYjaXJLL4pXafixRGWJ79KU3E2R7tjs/FWUOWqGY5O6E5pCRQzmJACBjl4qB4RLE0KJAm0lQ5Pi6qCrNWupyjEFviSu0rwjaBj9jlpmQak1GRqHYbvFf7XijYQSR0sWvehmXJKOJzGYqTmpWKDDDMPFNEVRzBpF8tH3oXmMirgGGPOqSDIoAXNV0ACZ7Kchu12QCWASlTko8YsgYKb5iGVo2XospmCLmP494qzVohPEBhT2Nc1JU1M/x0ml7llgxg4OqZX7Wh8rA9fjFGkNhkAckhd/VOyYeGhkQWC18tBltKxAi2QHQEWvqPmSHPQ5wo9aJ7siQzIaW7OMF6AkLETE2G6Io2Q03B3iN4ydhzSGRFGRyPMRNJNKnCgLguUawuXoJ40ioEhv3FRqADsHbO0E+FIKyjKDZiMSF8901OFLWmgCLQJbxzU3BZvX2HB17zUAqZhGBWUxBqkJ7n1BKEFBZjK9RJ/CJezQl5aMpM8gJLBi0kXS04/kQNYnKTZeTTTucx5cYbO/+VfnWUHTUFRHykkuwBMZ3UokxYRMgJ00SAMxb8QJ9KjhgMjY4xVtY4ILOJzFSd4ZYIl5+TKBjY6A29FKw2ZiP9fY7aPHlsi5Xb2/AB3QqN7pjxLSqCsCKy24W8YotJkDZh6oLBwCA/lDVNDkHCVPGFheSaevzohEDDR7IVPwUEuKXjVki4CTKdHvUqZ7dpxPmfVxU6ICXCO4DXmaCAmrWW72y83aum0l4za14uO6uwkEQuMXDE2QfFAwYCbE2shQzSxUhHkxtTwd+00xTBwR9P1l26oUhQCAOA/oYZpmAEoLXB3z/ANGptgn5xM6PzUuKkguoS4sOAJl80Qo+S8uA5svwEsy6GFhMfanSi6Eok2wQa3f4iBGJhVn2S8wbITdX0txNSsDmEdeNlRWyQJ5FYU9jfFL2tyh4n+faP6RxVlzay9OzqkCpXA4yyhKTeYmS9TLALhkzPYl8FKs0kAPWtoaIsLgd0j5MGQSJ+9FDSxATcYzaaSQFUAcPdTSKECoBc0wgJUiEI+lEPSXpNyDnU2c4mhPmXXlf1g/pkmlaEJ7KJPSXvRCSQHKF+6086IPUhLdZJjTjFKmc4R3QwV0zip2hI+xN5f8A2ltYOEosBZibvrU0/aS2t47E80RZIFDJ2SCCu5afBM+lTWVIls3QUDOphyupzbVe4D+nEm5amF4HlV6UzLhYkcMaiIpBqOqg4rKhIESuXzUVBWNfAxEdyBA2R0PckUII0Y/p0RFCshCUEGnynU5wPXpQ9hlkj/vHziVgDJi/7Bt6p4cbIRa8o7yvrzQR/T5pzrcEcRHD/wAqUzrtHMMuCZLealEKIIG+jb3iiotKJE5H4xK8ScowLuHVGy6NVP5XNMN5NEZCto4C3mgj+qhEOKWvuSLyrQ52Ux+R0OMFOGeUA812DmaZzMdDmr+WFCBdy3UfI0fzshuuVyv9ZE7E0sB1NMoWzRUJCiSzGrFCyuMG3GSuZUTMRq1Eb/BEVuYbdjMXp3IFC+WV+rmzUOBhsRujOWb/ANdMHXMAl7qCoqP5H//Z)
As x ≥ 0, y ≥ 0 and 100 - x - y ≥ 0 ⇒ x + y ≤ 100
60 - x ≥ 0, 50 - y ≥ 0 and x + y - 60 ≥ 0
⇒ x ≤ 60, y ≤ 50 and x + y ≥ 60
Total transportation cost Z can be calculated as:
Z = 6x + 3y + 2.5(100 - x - y) + 4(60 - x) + 2(50 - y) + 3(x + y - 60)
= 6x + 3y + 250 - 2.5x - 2.5y + 240 - 4x + 100 - 2y + 3x + 3y - 180
Z = 2.5x + 1.5y + 410
Mathematical formulation of given problem is as follows:
Minimize Z = 2.5x + 1.5y + 410 ….(1)
Subject to the constraints,
x + y ≤ 100 …..(2)
x ≤ 60 …..(3)
y ≤ 50 ….(4)
x + y ≥ 60 …(5)
x ≥ 0, y ≥ 0 ….(6)
Now let us graph the feasible region of the system of inequalities (2) to (6). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
![](data:image/png;base64,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)
The coordinates of the corner points A(60,0),B(60,40),C(50,50) and D(10,50).
![](data:image/png;base64,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)
Now, we find the minimum value of Z. According to table the minimum value of Z = 510 at point D (10,50).
Hence, the amount of grain delivered from A to D, E and F is 10 quintal, 50 quintals and 40 quintals respectively and from B to D,E and F is 50 quintal, 0 quintal and 0 quintal respectively.
Question 7.An oil company has two depots A and B with capacities of 7000 L and 4000 L respectively. The company is to supply oil to three petrol pumps, D, E and F whose requirements are 4500L, 3000L and 3500L respectively. The distances (in km) between the depots and the petrol pumps is given in the following table:
![](data:image/png;base64,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)
Assuming that the transportation cost of 10 liters of oil is Re 1 per km, how should the delivery be scheduled in order that the transportation cost is minimum? What is the minimum cost?
Answer:let x and y liters of oil be supplied by A to shop D and E respectively. Then 7000 - x - y will be supplied to F. Obviously x ≥ 0, y ≥ 0.
Since requirement at D is 4500L but supplied x quintal hence, 4500 - x is sent form B to D.
Similarly requirement at E is 3000L but supplied y quintal hence, 3000 - y is sent form B to E.
Similarly requirement at E is 3500 quintal but supplied 7000 - x - y quintal hence, 3500 - (7000 - x - y) i.e. x + y - 3500 is sent form B to E.
Diagrammatically it can be explained as:
![](data:image/jpeg;base64,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)
As x ≥ 0, y ≥ 0 and 7000 - x - y ≥ 0 ⇒ x + y ≤ 7000
4500 - x ≥ 0, 3000 - y ≥ 0 and x + y - 3500 ≥ 0
⇒ x ≤ 4500, y ≤ 3000 and x + y ≥ 3500
Cost of delivering 10L of petrol = Re.1
Then Cost of delivering 1L of petrol = Rs.1/10
Total transportation cost Z can be calculated as:
Z = ![](data:image/png;base64,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)
Z = 0.3x + 0.1y + 3950
Mathematical formulation of given problem is as follows:
Minimize Z = 0.3x + 0.1y + 3950 ….(1)
Subject to the constraints,
x + y ≤ 7000 …..(2)
x ≤ 4500 …..(3)
y ≤ 3000 ….(4)
x + y ≥ 3500 …(5)
x ≥ 0, y ≥ 0 ….(6)
Now let us graph the feasible region of the system of inequalities (2) to (6). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
![](data:image/png;base64,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)
The coordinates of the corner points A(3500,0),B(4500,0),C(4500,2500), D(4000,3000) and E(500,3000) .
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoUAAACVCAIAAAChAhcxAAAAAXNSR0IArs4c6QAAL+JJREFUeF7tnd/rXcX197/53rexNldBJNh4ISlYksZI0IKBpDW5UYzW0FwICtp6VaQxNnqnMRUlUKqpoYFQWppEoSKaWgPJRWvQGKVCQy6ipUjIVVuN/QP6vJ5nPSyns/eemf3j7M/+nPPeF4dz9plZs+a1Zs/a83vFf/7zn//RJQIiIAIiIAIisKQE/ndJU1fiIiACIiACIiAC/5eA/LHKgQiIgAiIgAgsPQH546W3gTQQAREQAREQgRU+frxixQrhEAEREAEREAERGJPAl1449Mea2zWmDaaTFq9iMv10zCFNREAEFodAWP2qv3px7K6cioAIiIAITJeA/PF0bSPNREAEREAEFoeA/PHi2Fo5FQEREAERmC4B+ePp2kaaiYAIiIAILA4B+ePFsbVyOkMCzz33HPMy/vznP88wjaFFT0fnY8eOrV27FoBcfB86o5InAsuDQAt//M9//vPll1/+3ve+Z48NF9+587e//W155HUgLS3v5cKmU+uV6xyFlOnborPHZHm557Z5HCo8lHbt2vXJJ5+YwE8//bQq2R6ipmtAzh999NH9999vCfGKQLrZbFIB7tu3b+PGjR7rRz/6EY9MNuKsA6C8v+WQKbJWniI5alXLlUtuG7IEL7Rhfu2116Izn3yPvBIlpLbwRPbtQ6xtvurDs9DFLv7279Uvf/nLX77xjW80JZmIOH9/GYTyfP3sZz8j/J/+9KfyKCOHlOn7A4+s/N3vfnfiRifLEymZP/zhD7OsTNWma6iHi1rua1/7WpTKT3/603TxMFtH17e//e3+haqPBKMaXmSNl56szH/84x+/+93vjEM28AgBsnjJVNVqUWYpIbWFh3LlWehMrCeEkPOXxBP0sZA5YwrZm2++6cmTSQorf/VUaL6jT6TWS0CW6fuXwOlbuZrHiehMhdvNe+E2KLpUo/3NZxK+//3vm0BqPH5Sv1lFn3ZjxIIkvtyE8IXsZN8wWulsliqPgg6ER3l7UyE75myyrKL3nvIUy0OiRugFsxGzeD1rZiY+q5k1f5xItzOxrP7ZAK398S9/+Uvi8NhkReOtrSxWnTdxTYjzsiLrpDwuxcgfidD329NiknkUw7+MNaL8ZapWVU+L6KZnbVoluXD5linM6erxxR/O6sudlQmeEL54lwPBwhxlOQ8bIPGoj2P6quGskFhtCCVYWRVpV/gvYQDuLSSrULCg47XoEbEQfmgvq4WtOKULZFhIkBA1iO2nJ2o/rVq0TEWvtlYkeLsNs5x+6FxmmDW0IhZWs5so5mXMQHnJ5N/IH9e656oO8Gl6EpuKZeKBsifar5JKxlIxZwzGsGD0fC6ssIVCrPw7z0L5IUnUgzxXqKc1xMsz29YfW/ioSjE10llI+2MrctHbiT0v5dWXPVyFJGuDRQW1ajViRQ9g1h93JtYnIxY3rCiK2se1ZqjqYU9IdIV2MnBh34L743Q3Ua1kf0iMtb8HmAK1mCxkNS3qFw9fkovwQaoV6O/7Tf64thOmv2m7SWjC5cU6281VAq3J9FXD1XYbuo2sgmuqx+25qgYIq9Tajil3VE2FJOy3rM0v6fprQa0/jrQKu9TIVMTBMpiosk2HyFWYp/Sqv/o8hol28MfpJ7G2+KXLRpMd0yXZSsiwztjsHrUga2+mdePlw3TzYCbETWm25nEof5No649ra+zCatzUjgpw+A4UeVOKXPS2kebT0x9X8VrlHyUale2sP+5PrFvd28Uf176ARMnbdAwM4x3aNggRmsqevdrmiBnJ6n3rJvJXOX/BdMnWI+QBfGzAJTSh8aqWWszTsnrQquPCXET+OMwUEkKByKw2O6xvBA72QPJJ1spfljsbviliwh+PbPqwLsBGxsc7VMxG1mTxSoF/KWlejRpt60Gx6F4OwzqFACbNOirC6rJanJoKpL9rooM5wrQ/9jax9x+6NzUdEGLF0opE2h8TLKr3iVX1KKHRLZUo0ahrwX9axMiR2IPZ9CRWC1jJA1Vb9ScKuTnj8MXCA7vtqi8idifKXZhKU5WdtYILsSRQLOrO8UrACq29DoYdFdknups/TruodKJNRiF3YReC2TfbDR6mFT682YxHEWvxWn0bMvfeSjd3VDDIAq/X4ftQbX5re4xa6VwSOKx+i9rHJSXSasmo14I8c9OfXqsoIxVrHwOr3cIKNBy35r7VVobbJGSnXXjI6P3ORNnNwlxE/jhypSYkUc1ZIQZFtt1ZYs7+YcICEUkbwfSR4QxOdNM8jdnIRw1rmxe1j5CVQ7OIFa2IvD3SPmpYrTKqBTJqmEbp1raPQ7b2TuZFkQqi2mDKwrd8ec0eFTySs7k53p1uDsMTbds+NvKJJ7FaFEseqFb+2BqXeIVafzYFfwwiTBlRgoxl00xW3rtrSKfjj6MqPSqBJXVR9eEqiUUYK71VvFaB115N/tgCh/0rE/HHpeudPv7446Y82/2rV6/yed1114XB7rzzTn7+9a9/9Ztf//rX03Ls3/Xr13swW/+wY8eOcMI6PyM5K1euLJFcDfPVr37VbxbmIp3QunXr0gFuuOEG3ijPnz/Pc8syCWbns+ZyCgskatWetekjw125cgU19u/fH5p71apVrtvWrVt5kA4dOsRNlhWxMOPkyZNp4GESn3/+OYExQRjl3nvv5efFixeb5FQLZNbKaZVuvvnmMADvByxNKXw6POKDDz7Id9Yc2p1f/epXlKjbbrvNfrLkY9OmTSwlOn78+B//+MduT0cYq/BJDKMM8kC5QJ4RLM6D85vf/CYCaGHIe7pydzj9aVQlWNLWfKeCilZh/fa3v+U+BZtnn9VHaQWi9TmPP/444aMVO7PIQlamFbmf//znfGIOHkMexlpbuKhwiaytoSI7YV5KFpURqwnv9u3bwzkNPAIQthfo1atX1xYMm9BAQXr11VezWR4zQJE/5t2B+mKC64zPnj07JqwB03rppZcoQ7xdUgVTpqk0KbUTdMmTMv3p06cxAcTef/9966OGGBUcdR/vNANaZ7mI4q0CA9kGGqwupX75yU9+4so///zz1pFO7WOtyWzzsXPGx3kSn3rqKfKI6amCO6uajmgvEH6ZT43e3tIScE4HDx4kTBOTf/3rXzNSPhIb1Sf2+LiL6qaDFTle73AHp06d+uyzzx577LFuorrFqsXLaxZPgTls2g/UrpQT3n6aDEf5MRtF5p4FsVbZLPLHd999N0LTVZ41QS5fvhwm/4c//IGf3/zmN1vpFAU2ydX+H9Dv2bOnj2SLazpff/31fM4uF1U9KUPPPPPMW2+9RUZwzBSgRPusfza7SRjf9F/5yldQtXb0AVaeC1oYPHU4ZjowqSB4p0lk8O9//7vXRNdccw3fo5fLV155hZs33XRTCSUrJF988UVJ4PIw3d7GHnjgAepEKqMTJ06Q1s6dOz1FyyN/UfukWzCFSnZ4Egd8oKh/sDIFI9G4bNr2wVtjiZ1DrOlMX0JI48KFC/xsSy+qBk3gD37wAyvYJJFtEUYN/dr+6oTVtmzZwr/4yzDMuXPnEi6qsAwQjCLH55EjR1544QUEZtv6VsX5RdxoxLBtNV6LN9SfHiPeRNOKRc/vTImVsy0aP06sP2Z8yIb3qxM3bOgoms9VnbVUO34clj+TbEMy4QQomkfh+HFk49puK0vLZ83YYGQ46axDLhAYZcpSicaPQ/X4C+XD7IwzcaCpKw9tm/4a3/RoYjOxfc6dNeyoyGzIlk++O16fSxWOtPnkjup0LV8n4/O5bH6NGzFbIG3oFyVNBxujReHQ6NnxYxsP81Jh3Ws+hY0kIq0SBiJpm+MaTasxHRwU5c1SaRo/tnE4n2ZocwxDMtknsapkyQNVMn5cuNQ42wGQmM+F8iXrj03b8HG2yYM+I8EmAIfkkWwPuDUqIrs0WTa833b8uGQ1rbOqVSBtFKsz7fWiRP+0P05LKMHrEsi4sYqm+/G0hvVJ1UYlxNrmtDB8WP0W+WPk1i5BcbdvCZcseungj5ske4lvmhhZxdH0uIbTK9rmIuuPo0QpLrVqDLt4o7AoWLCEPx7f9IkUrRK05y26ovnV0b/R9J+S9U7R611UIfoCXE+opz+26iC8TGDJrHvPTuRsqvNcTGaTP64uJKvqkF3oVS142QeqxB9XLR7eSXvZ8mehtpaLXE7VH9fqFr4bmSFcTu2K5LSSbf0x0rK7TdX649qHq9rUsWlcXB1mpEZvM1nrZPH6K074MEbT/UqEZIllVe0WIKx+i/qriUCPzaVLlzCMFUe7+G5v9PaT/oHqwv9sb0b6SXPJNmJvFQQX33nOu83OIG64oQE6h0oOnguUhJtty4D+dIzTLwo3J2kTEOjVaTudpwRd/zDjm54U6b2Hie9lwcsKxGwuCV2yVAfhtjPgpe86zGkYAFufOXMm7HIksFvEylIUIAvtxRdf9L077P1979692ViJAKhHCfdMmUqEt2609PXwww8TIJzJZeHppkYxY2ibojANKiGK4keiViyttY0VovA8HW2fxMEfqByP7v9jBQh45WDQGFRKS6QCicoq2L1AMmqwe/duLOty4Pz6668zymA92DO6agt5q4HwhGL2JFJUhhKYSCuN1yLaIBQXnHkwcVXREEOJkJkSK7Wyu3QidHPvyyhWeUt6GWWqv6rzZPql7fnvb4uw5w27lIzCDJioRE2TQIf28UwzYn0ebVdteW+cSnVonbD6LW0fl7p3hRMBEehNgMnSDz30kDVBeguTgGVPgBlPNq40kevo0aMlM7lqtSUjbSdwTSTXI6ghfzwCZCUhAnkC4YrMb33rW/QV44zbzuzNJ6MQItCPAC+LrHfqOUDTT4W5jS1/PLemVcaWFwG8r0+PsJHLcH3X8sqLtJ1jArb/TLiybo4zO3LWVng3yEROnx45/0pOBERABERABJaQwJdeOPTHkxqiWEI6i5Y0r2Iy/aIZXfkVARGYAoGw+lV/9RQsIh1EQAREQAQWnYD88aKXAOVfBERABERgCgTkj6dgBekgAiIgAiKw6ATkjxe9BCj/IiACIiACUyAwvD+2I1Y41rfbeTVTgBLqQC7ICzli1d3UdJM+IiACIiACc0OgnT/GJ9muBU3nheG9OI2L1ZPhbszs4Mqh8ebVuDh3naPTIm8dnVnteyOEoEmdvXBdSK0O3ES+hSFwoRNNxGKzWfJCju655575eMNoW3ZHM02Jfdsqr/AiIAIisGwItNq/2o71wDnZGYvVq3b34No9/9j4O4zetC9guJ2v75bgcKOjV7od0FESa743voZnYrfbcUxTcrTOTLfklXAREAERGJ9AWP2WnrdoWuKG7QANREQHWvGvnSNWPSGO81Lw0x6eL3aOTXhKWvbMtezRpN0OsCyPZdsn2QHMc3aV+ONElgcxTVbInDFXdkRABETANn74slVc3j62Uzw59s58WHT4OXL4i/t25nb6qjajs/7Y2uWhWEvOzqjnMpnRkSN2bnZCmfJYlv1uR5rkeCzx/z398SCmyQpZYkZKXgREQARmQCCsfluMH7/xxhvEZNtS9ringXvs2LGoU56jQ3F+nLqa7qw/efLkgQMHkFB+ejFzxJC5bdu2UPK6dev46SPEp0+f5uctt9wShuEn54wygN2kUnksy9drr722bIYiRlF0ENOUCBklN0pEBERABJaMQKk/ZioTDphOReY3oSyHweHn8Kyh4m+//XbkMqNs2TQrTufmbJDavfJ9GhdTsSLhiFqzZk0o0Nx55Guj87HtOPcrV66kARfGohFfPaF9yUw3bsIjmKbEvuNmWqmJgAiIwHgESv3xqVOncMB33XWXqbZ161Y+f/3rX4eaEmD9+vVZ3Ql2+PDh9957LxHy+PHjO3bsqDbBs8JnGmDDhg2ffPLJTJOYvvBpmmb63KShCIiACKQJlPpjO4Da3DAXDUoai1TNrZYAWd+7zaTF3VovpV00l71nHp9nw7osi5qU/VauXDkpfcZRZlmYZhwUSkUEREAEZkegyB/TJ8wB1LRrV61a5f2W3EEt2s1tlWP4+eDBg8Q6e/ZsbVyc/Z49e/D3pBgGuHr1avjT3HnU1Ry9H9jw8OrVq9NKdovVNuNzEH6mpimx7xwwVBZEQAREoJZAkT9OON0XXnihA9nLly9nY4U+0oaKaY6HsS5cuMBPvLvdtKHiSNVz587RFo98diikVazIYWSzMK8BBjdNiX3nFabyJQIiIAL/n0DJeicWGtWuGrI1o3QvmxDCcKc6IZyp1CwT8mAsHLKdPXz9Mb3TrJ7yhVKEtD06wqXM2fWphSuJbemzL1sqjGWZQp+mjVBmMA1+PJEAaUpsNNNk7TseDqUkAiIgAmMRCKvf/H4g5rGinbBMVVuS639Rpda67dp3n3D5so0WRxeiwi1HSvZvyu60xW4epBIpmY0VvrLUvnCMZbhZpZP2x+OYpsS+s8q/5IqACIjAEhFo54+bduPyNrE3GZv2A8Ft4/MIZjW7NZfDvNMgJq7vy4i/JLy3pz0kVba1oriQhhevAuSmJ0TgaBOx6AXCo6djhS8fi7YfyGimAXKJfZfokVGyIiACIjATAqE/XkEK5uGYqOXfa1u02ZsMK954441swVG7tjgbfYQAHGuxf/9+fExiRLlJDY5VYDT60qVLtgJ7nq7+pp8nGsqLCIiACIxGIKx+i+ZzFWqGo2KjD+ZdhwuZCuOOE4wdS2g0d3DG5Ih8kbv5c8bjkFcqIiACIiACaQJDto9JiSbypk2b+MJ2H1NzXejGei26rLM7ekbIppypQcq32seDYJQQERABEWhLIKx+/8sftxWk8CIgAiIgAiIgAn0IfDlqPOD4cR+FFHcJCah9vITwlbQIiMAiE5jV+PEiM1XeRUAEREAERKAPgSHnc/XRQ3FFQAREQAREYJEJyB8vsvWVdxEQAREQgakQkD+eiiWkhwiIgAiIwCITGN4fs1SXAeqNGze2OopxsjYgF+SFHH300UeTVVKKiYAIiIAILHcCRf7YXGx03X///SdPnozyj/d64IEH2LGSLbpq1x+7e4v2DGH3q2oS3Anl4xFJ1IKtXbv2ueeeq9LnJn9ZGAIXOtFELHJBXsjRPffcMx9vGG2LbNY0HMfJxmf21mKm4eDqKqusaUrs21Z5hRcBERCBZUMgPCyhaXdODmJqyo+f0WRx7WSI6KaL5TgHO16pGsY3r44SCjevtlOhwis65aL8ZIgwpyWxjEDtjtkz2dJ0XKFkLZFg1jS1ATB0K8g6T2Jcmys1ERCBSRAIq9/8+U6oXPVGfiRi6KJwt7jM8JDEKLt2AJT5v8hnW52ewJM9j6/VyYmhmyddtDJ9yIKpFx4/ZYHRkGAEmIQNB1WixB+nTUMx8KM7+GJvXW7iEtNk7TtojiVMBERABCZBYAB/7E6ac5k8T03nO1kAPJwdoVjbhs76Y5SOzh625FwBExudv0SKtUdAus7lsexsqEU738leRNIOu1qoIxOXQM7adxKPjpQQAREQgUEJhLVr0fhxtbOaIcOnn36aZtDOnTv93zNnzuD8aneHZnzx0KFDBLj55ps7dOXbYPO2bdvCuOvWreOnjxCfPn2an5wuFYbh52effYa2TYmWx7J8vfbaax30X6gozCo4cOAAZeO2226zjGchl9h3oRgqsyIgAgtIoIU/fvzxx33KFU1Vzjt67LHHwklbnJ4UuUwDeuzYMU45pGWZdcYuv3ay2Jo1a0ILWXUf+dro7KYtW7YQ5sqVK2nTFsaipXj+/PkFLCVkOW0aY2Jhdu/ezUFY1TM3s5BL7LuY8JVrERCBRSDQwh9XcezatYvJt36fluj69eujYDhjguGMcbHlQI8fP75jxw7ilkcZIeSGDRsYOB8hoSknkTUNxeDw4cMc8DXlXEg3ERABEZgagRb+OJpdbNN2aCWnvebRo0fJMy7ZG1i0s7lz++23h8uZaE55nzw+z0YcWTYzKV4rV66clD7jKFNuGrOgzZTmdWqyx2CPw02piIAIiEArAi38cSSXzueDBw9yc/AhVTo29+zZQ+cwLa0w0atXr4Y/rbqPekGjZa82crl69eo0lG6xWoGej8BNpglz5wXj7Nmz4f0s5BL7zgdG5UIEREAEqgS6++NCmmHrytpP4eTbhJCw+rahYnpKw/AXLlzgp49J21DxqVOnwjDnzp2jrRb57DBAq1iRwygkMH/BsvuiXL58uRXkEvvOH0blSAREQARCAt39MdNof/zjHyPrrrvuMol4vg8//LADX3Zuomvad/tiihY/mTkVbjTB+lT6sX3jJxrHTzzxBGlt3brVUrTABLB2Mz6D77Swo3Fr20bK+9gLY1kSH3zwARPZOmRw+UYpMQ1I4ekT67CjDTRs3ry53DRZ+y5fhtJcBERABIoI+KgtoZtWVSX256Ia9Vi23Ud2aVZ1/bHdiS5brOzSSvZvyu60xW4e9t4QKpmNFSIK85vN6XIJkDB9iWlqy1m0oUoWcol9lwtP6SkCIiAChQTC6rfF/lxRtUvLMtocI70fiCtX9cc0fInrrWHbw4ubUX6osm0XJy7aqbW7V3LTm7AEDj060mxPj2iXTetCT8QyNRZzP5AS00AGezlAZvnV7pqShVxi38IirmAiIAIisCwIhP54BRqbh6MX178XtawrgegivvHGG9mCo7r2tJvAwWOxLQkrofExiRHlpkRZ2cVo9KVLl2rPyRhc1TEF9jf9mNoqLREQARGYGwJh9dt9/LiKA0fFRhCsgJrsQhd2LKHR3MEZkyPyRe7mzxnPTbFWRkRABERgWRMYsn0MCJrImzZt4gvbQUzNdaHbqlWr6Fyt3dEzYcUpZ2qQwqf28SAYJUQEREAE2hIIq9+B/TGq0JRkrw8GEZuOQG6r7tKGxxnTU81kb0Y3s/t9Lq2qnVOXP+6MThFFQAREoA+BRn/cR6jiioAIiIAIiIAItCXw5SyuAedztVVC4SdCQO3jiRhCaoiACCwagVnN51o0jsqvCIiACIiACAxFYMj51UPpJDkiIAIiIAIisGgE5I8XzeLKrwiIgAiIwBQJyB9P0SrSSQREQAREYNEIDO+PWSB07f+7Pvroo0Wj2Se/HMnAwH50+kUfgYorAiIgAiKwjAi08Mc42pdffpnFuLgNu/jOHT/Yx7L96KOPcqrSmTNnmlbrcvgPcTk4KMTETxcbfgm3+rIjm/D0BODTz3oK5XC4kJ3gxMUXPzMqYRLC4AVNrGWqGqtWN0K2SpoXFBIyUWvXro0I8BebeHOmJEgnVYBCi4ccXElsVMsnzGBWCNLSfCbFRMqIgAiIwPAEwsOLErtvsxtG4qhBj2gnQdWe9GBh/JyfKEztOUKIQqBF5Ggm9hiJ8s+dUGeOMagCYkOu9K7itUyjWLVhOADDJWeTLjy/CJkcp0Fmx9wJndwlkgtPvQw5REavIgpNnBVSyGdMLEpLBERABGZNIKx+i853wj2YM8b/hY4KZ8lZSfzlGqfdiR0ARZSqz64e+hRRsLgoYOc+8WnuOTxKCE/GHUJaXIsSqldL1g6qMrHk1N4YIk/PndD7VuVkk7aTqRBuvhZ0FiU6xir7QjOLwlHijxPpluhs/jghpJDPLLIvmSIgAiKwVARa+2NzbGmHRGZo4pi7rc2YtSD5rK2+s/7YKvTQe1lyfiCxiY2O3bVaPjp1McvdmnphsHT2S5KuvhkYVX978OR4Fci+Q2Sz0CrAFPxxOZ9WWVNgERABEZgygbD6LRo//v3vf0+cl156yRxV0/Xuu+/y13333VcNwIjsrl278D2d5ytxvBJeKjyaycan2Vnakjt79iyf3/nOd8LU169fz8+LFy+mNa/+29S/Wisnm7SNgm/bti2Mvm7dOn5WZ73de++9vHYs1Gy4VnzamlLhRUAERGBZECjyx1VfWJs35nDRB1udxoVr2b17Ny3Xhx9+OA2Fgyh8KlZ1WhNzoKLoeE1cV3jzuuuuC39u3ryZn59++mm5MSzdBx54IIoCBNPNppJV/WU26TVr1oQyb7vtNn5Gs+G4Yzp3eIcoz2OHkD5jizeq2llyjz/+uE9V45xpJt9VU0kLKeTTQXlFEQEREIHpEyjyx2Sj6gurefv8889vueWW6D5+64477qASzzavw4i0eh955BHc3sgE0faJJ57g1SHRjmf2+KFDh8jUjJqwN910U9t3iDEpMQN8x44drM5qSpQ3pP379zOhutYlW6yskDFzpLREQAREYAoESv3xxx9/3E1dmpXmwLxtRCMYUdac8uVMe/bs8S5+ZjwxzExTm1gz8nm1ecHHNL06hMMPjEYzLE2mnn322W5M0rGmdm4052Z69vG1NtIfvirR0A/5MOOPIXDeqF599VXPaVbILEhKpgiIgAgsIwJF/ti6has9qzPKJw6J5unevXuR/+9//9tTqba3rCM9VOOLL74If9rI7vXXX59VlW5qRrhL2vF0yFvrkP6AVklfvXo1DG/vIuGIeFbJJQ+Atrw5UR54HWlSZvv27QcPHuTfKL8evknIHPBZcgNJAREQgeVLoMgf33333VGTqDzDYcPXWlHh/GobQ629otoZH0CTK3wnsKazL0q2Ydc33ngjlPbhhx/y03qAmy7cPG6Y7nEa5YWd6tGbQTZpyyadtKEOFy5c4Gd1uD3RzVuOfaYhsxpGb0W1yoRCWvGZadYkXAREQASWjID3NKJB06TwxPpjpkz74hx6celkzs4sr6534o4tAra1uXzaWqBwZ4yh1h/b6mdfFkW7H/1JKLEminwRywPwxV4Cwv0uhlp/7O8r4brqLNKeARKmJ4+w8kXn4LL12eHiNwBiHV+KRmCj4Xu5lAjR+uOeRlR0ERCB5UggrH6L9gMhk7XbJ/lLhFEwl5ld7Fvrj2vfR0KfNNT+XOZKXUlTpvZyd1u79gk54S5aQ+3PBUYboM1iHLDkpf1xFU70+lJLL1wIXrv5WiRE+3MNaFCJEgERWC4Euvhja7ZSsYbOie/4YHdL6f1AnE7VH9sELmteW+XOd29deUTbPMvC8Ol7XVUnE5mQaDcxy4Ldj5RJ+2PyRfvYO8ZpDsKhuqWlzWNqStreaawVyGVCakvMpPYDodWLid3ohj3aU4yMc9MH8tE/atyXCCnns1weM+kpAiIgAlkCoT9eQWjzEMx29u9NTcbsfVa5nDt37tKlS1ObJGyas3CWtTp4i87bkmQJ9AzAJC/mn+OqGXfvKao8+iCmL09OIUVABERABKqet2g+Vzm4J598kpm3R44cKY8yZsh33nmHFt5knTEonn76aTR88MEHx8SitERABERABJacwMD+mImydMmytnjMdcPlEN9++20/YKo81mghWXPFCi6WNU+zd2E0DkpIBERABBaQwH/1Vy9g/pVlERABERABEVhCAl+OGg87fryEWVLSnQlo/LgzOkUUAREQgT4Ewup34P7qPmoprgiIgAiIgAgsLAH544U1vTIuAiIgAiIwIQLyxxMyhlQRAREQARFYWALyxwtremVcBERABERgQgRm5Y/ZGIRh6sQpuRNiMBlVWCR27bXXctR09sCGyagsRURABERABIYhUOSP2TTKTy+2Lxs3buQEXD+9ONLF1tGyz2LTzhv4aYTgs6OIOCSiWBK4peeee66aS27yl4UhcHWhc4mQSCzHRu3bt49MedLkruoU+yeNTCTjdEmIzygVzno6c+YMu0s++uijw5h3CCn2alW9amWTQcMYlY0SIR0MN0T+JEMEREAEpkHAd9dEnaadNhOHLoTHBlh0NnZmh6nw/J9IrB+9EIUpOVGgupsHaYXbKZcIqWaz6cSIMGT/pEuOxCBFO32hun13dh/UzgESpkdmLZzaKGEGI/2zQroZrnOWFVEEREAEpkAgrEuLzneqPZGJIxbsaAe+hLlKuxM/c4KIkT/OnrhncUnU6no7XoI74TtBVkitAYiF2tUTFd2pDJJ0yZGRJS80g5ehEn9ckqidCGJGqfXHCSHdDFeilcKIgAiIwGQJDOCPLW/epgkPB6RGDg9QCilYeHOfVX/MHT9K2WKZA+PTfpqnj84OQmB46HJWSKFVoreKQZK2NmLUmucOrijSyg5pjo5RKtS8Q7BB/LEdvYWJa1/ILO8J3YYyXIfsK4oIiIAILBWBsGIsGj9u6llnvPOll17i3xMnTlgYhgA5T+Khhx6qRmGM9o477ti2bZtFiS4bbuTf8P66detMpt08ffo0n7fccksYhp+kiHBulghpykt4n2OgDhw4wFsF23EPmDRj6rxw3HDDDZ4WAPl+/vz5SKs777yTO6dOnSrRdgphGH0/dOgQg9+Wo7bXUIZrm67Ci4AIiMB0CPTyx2Rj69atfH7wwQeWpXfffZfPW2+9Ncoh03xoBeKNXnzxxUTm16xZE/5r7tB8rV+hP+Pmli1b+Lxy5YoHKBHSpIPNWtq9e/fevXvfeuutKFj/pJmJFsmk4Ug7OLppGZ/UmRw+n4s5dLyvhAozO2///v30W2SdcUIIAvsYbjpPlDQRAREQgW4E+vrj6CSiq1evokdUL+OMbSo1Hm5ZnFxEg/vw4cPvvfdeN6aDxKJ1Hr2IDCK2v5Djx49zhrSvZOPLrl272h4pHQnpr5UkiIAIiMByJ9DXH5eslL148SJdslyrVq3yFhLg6L/lZ+2ipqXCGo6L43WaFnSNoN50Xlx4i/KRFZryNjzMSi2DcPToUT5xyW5ZTtvkzu23384dB5UWMgJPJSECIiACEyfQ1x/bGOeGDRsGyac1r/0ydxj1EkdvADaovHr1ao9VIiStLe37gwcPEubs2bNhyP5JV19fbFB5EHojCMEWe/bsoY+dLoTOyTUJ6W+4ziopogiIgAgsOYFe/pgBTmsnPfjgg4mcMBpanbpGeFvvRP3OdxsxpRszlHPhwgV+eu+3DRVHs5zOnTvHtF7z2SVCColfvnw5DDlI0uSXToKwF9pGiOmarmpV0vFQmJfBg4W6hQ3fcBq8rXdKJB0KGdBwg2dWAkVABERgJALuKUmvacJ37fpj+i2r649thVK4/KlJpvtjD5BdgTrIImCSe/PNN0k9XFuFR2QE1NcXEcCytiTrjw0IqVf3WpnRjPyE6bEyagDEkgaRLS9O7PdSXe9UIiRr/RnlXWJFQAREYAkJhNVvi/1Aal8Qos1AzGX6iuFEJqt1eskOTf03yUIlW90bKlmbtcgd9k+6cH8uNLQXoBKMgxSjtD+uwrF1xk1J1/rjrJAS6w+SWQkRAREQgekQGMAf06DEP9Xu6ZjYDyREUNvGolK2dpK1X6nZq9S46QOuBK46hqwQ6x/GO7pw2n9kx8Vac3kWSdueYtb4tq1RQjU8xensB0KDmNcC3+3SdE5vVFL1x4VCsoabziMkTURABERgEAKhP16BRPN/zIb177XtxcKbzJdmhi2u2jfTKIw4TjCGLZnmjVOp3ZZkHB3SqaDhjTfeyD4n1QXQM1JvKNPPSD2JFQEREIF5JRBWv73mc9UCYm4Xrainn356mvhsVfHDDz88TfXQ6siRI8xefvLJJyeroRQTAREQAREYnMDw/piFs88++yzLeDh1cXB1+wt855136I7O7iTVP6FuEphxTe8C/fDT7F3olinFEgEREAERyBIYvr/akmRDLlxy222bsurOdwCcMVt8cy4yjfgx9wNRf/V8lyvlTgREYLIEwur3v/zxZDWWYiIgAiIgAiIwlwS+nMU1+HyuueQ135lS+3i+7avciYAITJbAbOdzTTbbUkwEREAEREAEJktg+Plck82qFBMBERABERCByRKQP56saaSYCIiACIjAAhGQP14gYyurIiACIiACkyUwsD9mbymW63DZyUW6IACTjRs3MmgvJioPIiACIiACTQSK/DHnEPtp89EXdscMRT/66KPsLXXmzBnfcKMpbhSRn2vXrjXh999/f9V1cYf7FoCQUfTa7HGy4b59+8wXWixOh6yeYzhI0gkhrCRm50s2x77nnnumfIpiyUNy7NgxSLK4vCmwv3zY2dXhNQjnEiU7hCFHVkKqce0vLv/L7lQz2JQuGSd8SYntoLmiiIAIzA8B3xGbLDXtjm3HDdVe4ZEP1WMZ/aiiatwwYv+jk2o191MQwtTZnCsMPEjSWSHOofaEjEE2Je8jJGH6UCy7uxjJpsMWwwOsorNGsoiW9nwnLyrROSJWpO38D0dhgWsPU6m1gh2wMU3T9yk2iisCItCfQFi3tDhvMVuhUE9Rc0UHFtU66TAPQ51qXOXCrpPo7AdA8cVOdhr2VOMS/U23Wj79zdlfQok/tmzawVNN/hjgdgBU5K5KEC3t+cfmYvkMT8U2k9lVgqi/ISRBBERg0QjMxB97fR3RzPpjaz1E7RKqda6w7R5VlBwCSKy2JwRHRwEOknSJEMsIpzpWczqFwpd1NtZ4tQOhm/yxnSNJyKbzj8cxcTee3uQNDWRFl8/IH9f+DE/S5LUPW7smtaWOALzc2BGffFpJBpG9MnJFZ3FWsQ8ithsuxRIBERiKQFj9Fo0fWwWRvt59910C3HfffbmA8f+nT5/mFscLhn/wk3FoBoC5aQN127ZtCwOsW7eOn61mSJ08efLAgQPUd35UwyBJZ4W42tu3b+f7a6+91hbR0obHCuyqDf/ECZWM0x86dCicNxDqnEU0lIl7gqJg4Gv9ZK1f/OIX/Cw82IMjMiFAoUWH8+fP796920pv07Vjx479+/dzMjQB+HzkkUcYvd61axdxLQrSnnrqqbY5mpHYtmoovAiIQAcCLfwx5w5VZ3X5LBXqYppHTecmeVwqHeru6rSmG264IdR+y5Yt/Lxy5YrfXLNmTRjAasl0lefhTW2qyL1791YPFR4k6awQU4b63SvcDtYaPwqWoieZBtyLL77YlDqTvHAttO3Sp2ZlEfUxcZNuHDLW6qUNZ4x3JEcUrePHj5efegkiaxNbQxnHfOrUqYS9eFggZoM71tIlXVrMfHKHRjkBUKOtxWcktq0aCi8CItCBQAt/nJb++eefR23c2vBUN9TdzFAdf6YxVeThw4ft/OOlujZs2GBNomVxYSObSs1LTNN5U/gMWnWTPchr69atNO7LXbI3kZ9//vnyxjGI3n//fev/AJSdrn316tWElV9//XXWCxhVjgznE6/8zDPP2FsLalgXUdtyMiOxbdVQeBEQgQ4EWvjj2vlce/bsSadKzRL2s9OGoMeYNuKrr77aQd1uUUwBGwSlQ698pUq35BKxVq5cObjM2Qm8ePEiluJatWqVd42QHCdp+gKeo0ePcgeX7AHoC+HO7bffHq4Rmp2Sacm4N07jxiUzWlGogzWR6S4ubxxHktuerm1e2Xr1B7xmJHZADSVKBEQgJNDCHw8CjjbEwYMHERW1HqLmstVNq1ev9kSj8OZToy7QtIbUkpb02bNnw5CDJJ0VMgi9ZS0ki6itiZvWxEf3GZqlocl7WKFLtiZyq8bxsraLlBcBEZgIgbH9Mdn+4osvwszbUHE02Hbu3Dnast53RwAG88JYFy5c4Gfbhsjly5cHTzqrf5hiug9zImXC1Yj6NqybgX9tvZN1jdCVHc0zDOf9mqgsIpsN0NbEhfMb0YeyxIis9SeXXGSqOs+gJKLCiIAIiEBnAoP542uuuQYnWtWDCVzMqfGJV7RRmFdFsM2bN1tgWz3CzlnW5KUVxXcaNIyuuTSmFNGF6LtrEfKJJ57gX0YHPQySoy2W2JnLJuZYGAIgYfCkS/R3JT/44ANb4rJQVwmiEhN3gMbI8SuvvHLp0qXCadIdkhgnCqM8DBPYM0KRZh4liwXGSVqpiIAIjEQgXOPb1OAo2Z/LFgT75huh2GpObCWrX4Ns3mRbVYQrkmsJziLprP4hDRxPYcNutGCAKk/LXqES4avrjwmcRTSj/blQxmYsp6/0jh8l648j+VDy+Ra1C4Wj7b2qVKNETUh42a5hLqcWe1ZsDoz+FwERmC2BsPodrH186623IvfEiRNRrcEELupibxTyms9c3GglKz+pTTwMHovVU+HYMP3S3LEtnLgIaZNRw7Tefvttfu7cudNvjpZ0Vn9TycYv77rrrpFetaaUTBZRiYk7ZIhO9VaTDDokMU4UMmId7yRnDxGL98ZJWqmIgAiMQ2CFjQhy0dnr37ulzdoYuqzpG2xaG9NNbEksermZA4zjT+xZUSJnpmGWkE86X/1NP1NuEi4CIiAC80ogrH4Hax8Di/UhjPseOXJkfHC2qtjWfU7zYuSP8T/aNOO/rEwTiLQSAREQAREICQzZPkYuk7CYJctYYNuZzz2twp5f9FezJ0NPOTOKTvN906ZNCOe9YYL+WO3jGdldYkVABESgvHvyv/yxwImACIiACIiACIxJ4MtR455jxmMqrbREQAREQAREYF4JDDl+PK+MlC8REAEREAERmDUB+eNZE5Z8ERABERABEcgT+D/wZd8ibt5l4wAAAABJRU5ErkJggg==)
Now, we find the minimum value of Z. According to table the minimum value of Z = 4400 at point E (500,3000).
Hence, the amount of oil delivered from A to D, E and F is 500L, 3000L and 3500L quintals respectively and from B to D,E and F is 4000L, 0 L and 0 L respectively.
Question 8.A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine.
If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden?
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)
Answer:let x and y be the bags of brands P and Q respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Minimize Z = 3x + 3.5y ….(1)
Subject to the constraints,
x + 2y ≤ 240 …..(2)
3x + 1.5y ≤ 270 ⇒ x + 0.5y=90 …..(3)
1.5x + 2y ≤ 310 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
![](data:image/png;base64,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)
The coordinates of the corner points A(140,50),B(20,40) and C(40,100).
![](data:image/png;base64,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)
Now, we find the minimum value of Z. According to table the minimum value of Z = 470 at point C (40,100).
Hence, 40 and 100 be be the bags of brands P and Q respectively to be added to the garden to minimize the amount of nitrogen.
Question 9.Refer to Question 8. If the grower wants to maximise the amount of nitrogen added to the garden, how many bags of each brand should be added? What is the maximum amount of nitrogen added?
Answer:let x and y be the bags of brands P and Q respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Maximize Z = 3x + 3.5y ….(1)
Subject to the constraints,
x + 2y ≤ 240 …..(2)
3x + 1.5y ≤ 270 ⇒ x + 0.5y=90 …..(3)
1.5x + 2y ≤ 310 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVUAAAEdCAYAAAC8B/QvAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAACKISURBVHja7Z1NjhtHsoDnAjMXkHshWAvPssctyYCgzWM/yssRWnRLC3tBcyTAbXhDCI2ZB6HpjfXWgtoXEDA/y9EF5kkn0A2sG/gIfE6ysxlMZlblX1Vlsb5FAN1kMSqrKvKryMjMiN/9+OOPv0MQBEHySCNK//Lg4O+3bh4stXz6YPp3+3fHH3+4uLjBg0AQBKjWyGI+uXP35sGvd0/nf7NB1/Y5giAIUK2Qi9nxw1s3D3+dzBd3tmA7/vaSm48gCFANlPPz89+f3j54/+ntR++fnp//YfX/0eFbCVkEQRCgGhEG+HJ28VB5rgz7EQQBqomiYqiffn74y92bow9MTCEIAlQzeat4qQiCANUMcnHx9Y0HNz/5qEIA3HQEQYAqUEUQBAGqCIIgewfV+eTz/3HtrkIQBAGqCIIgCFBFEAQBqgiCIEAVQRAEqCIIgiClQFXN6nMzEQRBMkIVsCIIgmSGKmBFEASoZoYqcEUQBKg2AFXAiiAIUM0MVcCKIAhQbWD4D1wRBAGqmaCK14ogCFDNAFigiiAIUM0MVmKsCIIAVaCKIAhSFlQBK4IgQLUhqOq/udkIggDVjN4qNxtBkMFC9S8PDv5+93T+N/nZxez4oQakLuC3mE/u3L158Outm4e/TuaLO0AVQRCganygC/VJqK6roR5+UOBc/z1693Qx/+z06PCt/mx89OjN0/PzP1SFARAEQQbpqSqwSqgqj/TO0eStgub5+fnvHx+N3sxmx2eyMqrybm0lqIEqgiCDhuq//vmP5eV3Xyzvf/dqqf5ey6vl2b2D9Wevny3vn7zYOcb8v2r2f6MXQRCkH5IEVdNTlfHTT28/eq88VvMY22+a9lZDLnRf9dJW9GILZen1hurFdDI6nU///ODmJx/VsD8GqrnBinHSVvRiC72EqhlTVRNUj7/67598YqpAFePkeaEXqFqgevfm6MMPFxc3NFSfzOcjPfsvoeuCahNhAIyTtqIXWygeqmrCScPPHN6bn9etUwWqGCfPC714qg00CqhinDwv9ALVBqCaG6wYJ21FL7YAVIEqbUUvdgtU80E1J1gxTtqKXmwBqAJV2ope7Bao5oVqLrBinLQVvdgCUAWqtBW92O1QoNpU2ROXrtTzYJy0Fb3YQq+gmguwQBXj5Hmhd7DD/zahmgpWjJO2ohdb6CVUmxr+A1Xail5sAU81M1RTwIpx0lb0YgvFQ1Vm7Teht8pQdfvgfUjxP6CKcfK80DtoqOosVWbCaQ0+mUNVpwH0Kf7n482GghXjpK3oxRZ64anasvjrstUSfqpstW/xP6CKcfK80AtUrz7TSaofjA/eyTirb0kVX1gCVdqKXmxhEFBdJagej95Np+thvqpT5UpknQrVELBinLQVvdhCb6Eq/zdDARqE8riYjQRAlbaiF1vYS6iqyar7373a1LxePFzeOnlx/f/191efaxguTg6Wk8VuvWz1nW9tba2LOuMIgpQkWT3V9ZD/8IOa5Zcz/vJvDcPY2f8Yb5U3Pm1FL7ZQvKfqKvynZvr153KGX65TdQ3xQyegfMGKcdJW9GILvRj+pzbAtnkAqGKcPC/0AtVMYI3ZLeUDVoyTtqIXWxgMVCUYgSrGyfNCL1DNKE2BFeOkrejFFgYN1dyxVYyTtqIXWxgsVGM91qrfYJy0Fb3YwqChGuO1AlXail5sAahWQNV3aO9zLMZJW9GLLQDVCLACVdqKXmwBqHpANSQcYDsG46St6MUWgGqgNxoD1c3W2e3sWJ/efvTelptA5jqQ23FlAm4lspyMS9duOw5/0WVmzPbKnAp153ClVaQjoRdbAKpJYPVtq4aTzlOg/zdBqWClP1tBcPztpdKrwWxLeWj+ziYbOG9qd5ntVfrM2l5V55Df0ZHQC1SBqvexvjHYEKhuQHf88YeLixv6fwmt+XQ6Up6h1ruC2pW3qKsfXP925WWO3un/rWA1PFHZXnXu8Wx2Jr/3OYdZsoaOhF5soQdQtXlEtqHy9lA7vpqqC56uVQOxUFXXpSFq+97Uu4LuFVTl33W/r4Oq+vzL8fSl+b3POdT9vnM0eauPoSOhF6gWDlVXNdUNJD75qL/LWU3V12uVn/lAdSumKrxS0yu03UD5AjGH4ilQnY2PX6rzmt/7nKPK+6UjoRdb6FE1VQ2D06/+dCkndXJVU/UFayhUTU9VD/9Nr9C8B+ZLIhdU1Xn1b2Kgan5GR0IvUO0pVJVn92R6MTK9t5yF/3zDAbLkSghU9eSR+qwOqtqblL9NH/6/Wpres0z87XMOoIpeoLoHUFUd+fH40U+qs3cBVRtc69a3uuKRKv5bB1UVAjFhaYYLqsIHvkN183ufcwBV9ALVPYDqxXQykkPUrqBaBVbzHK4lVXr474Kigq0qaij/1zrM5U6uybxYqPqcg5gqeoFqz6Fqm/DRE1lVMdWYEtW5oOpa/C9XKNg8WXXdu7/ZLMHaWpgvrltP4EnP12yDOk/w4n/LOlhm/9ELVHsI1Z0S1UK2v3u1PLv3xfLs9W9/v362vH/v2fLyn2klqn1LWNskWJ8qse1oc4xcfvdsuWi4TK6rDDiCIIWWqHZVU3UN8ZtYp5pj+O8rtp1RoW877V3WhQNS36LsqEIvnmpPPdXcDcoJ1SqwxupTYQwJqxIfOHv/0QtUgWpjUG0yZotx0lb0YguDhKpsq4bpu//7TxawYpy0Fb3YAlC9gmoOsGKctBW92MKgoarPoaEqwRpzboyTtqIXWwCqhrea4rVinLQVvdjC4KFq81ZjwYpx0lb0YgtAtcJbDQUrxklb0YstZIFqk1tL27pQF1RD4Ipx0lb0YgtA1cNb9QUrxklb0YstZBv+N7GYvjSo1oEV46St6MUWGoVqKlzbhGoMWEOqtGKcdCT0cg+CoFqXCSoGkKVC1eW1Ypy0Fb3YQiNQzRUWaBuqqWDFOGkrerGFbFBV+TpVNiQNmO0k1ccfd5JV16T96wtUU3dhYZzABL3cgx2o6sz3MsXc88nx9xqYKp+nzm5vwtVVnrorqMaCNVdSFowTmKAXqK5EJal2JVuWdZ10KRWfkEDfoNoUWIEqMEEvUN2SdU2l0TsFVZk0uS7e2uVwuiSwAlVggl6guuOpjk/nZzpUYFZSdcG1r1DNHWcFqsAEvUB1S2anJ2c6blpVnrqJDQQpF5oK1pKTX9OR0Ist9BSqCpqynHNVeWoXWLsaTueAaqnJr+lI6MUWegBVszz19mcvlmerv/3KU7s2E7RdXjYHVM1wAGV7EYQS1ZVQlXFR7a0qD3QbiJs1qT7lqWVMNbfXGnKhubzV0pJf452gF1so3FNtI59qLriGtjUnVEtJfk1HQi+2AFSdcG0Dql2CFagCE/QC1UahmgrXmLbmhmrXya/pSOjFFoBqNrjGQrUrsAJVYIJeoNoqVEPhWhpUu0h+TUdCL7YAVKPAatMR29a2wNpG8ms6EnqxBaCaDa6lQrXN5Nd0JPRiC0A1G1xT2toFWIEqMEEvUC0GqiFhgZKg2nTyazoSerEFoFoMXNsEa59ytNKR0IstDBCquq0pYG0bqn3J0UpHQi+2MGCoujzXoYCVjoRebAGoNnqhoXDtAqql52ilI6EXWwCqv0uBa5/BSkdCL7YAVFu9UN/ChF1BNRWsdCT0YgtAtfUL9Vkp0CVUU5Zd0ZHQiy0UDtXFycFOORVXMurQJNVd38AquHbtrZaUo5WOhF5sIRNUdeZ/CdXz8/Pfnx4dvlXQVCWqx0eP3qjif67Pm4Lq6ny3D96bUJR1sVLhWgJUS8jRSkdCL7aQ0VM1C/+5CvzVFf7LCVUF7Qc3P/loAl9daNV5Y+AqpQ/hADoSerGFnkHVVYq6qkR1bqiu62Tthhj0hc7Gxy9/uLi4Eau/VLB2laOVjoRebKFAqOYqUa29VJs3qi/0YjoZVcV09xmsdCT0Ygs9gKosUe36v+64KkgFlYatKX+9ksXDld7JIq2EdalQlWClVDCC9KhEdYkx1apJMHWhagLryensLPVNVBdfLcljbTpHK94JerGFBof/cpZfLaG6czR5a87+y8+biKnOxoc/24b36kIX86efPZ1f/DHHjataFVBqOICOhF6gWjBU9ZIqc5a963WqLm+1qY0KrvhviasD6EjoBaqFe6ql7qjaAPxg+entR+8VYHVb5Xe2l0LMDfTZ1lrK9ta+JL8GJugFqgVB1X6hL5Z6/aoZz30+Of4+dkWAvgchYO1r7gA6EnqxBaB67bneF15rEzcwJMNV13DtQ/JrYIJeoFooVPWWVbWEq+kbGJqXdV/ASkdCL7YwIKiqCTW1nKuNGxhbSYDk18AEvUC1F1BVXurj8aOf5ETVehure31paG4A8x6kFBXsCq4lJr8GJugFqgVCVS2vejKZf63bqv5Xe//N2KpeHqaAOp/P/5hyA3OUwu5bLSw6EnqxhQFBdTpdz+rLtipvVS2j2qQIPP4Ym2TFVfsq9R50AdeSkl8DE/QC1QKh6mqrTA8ot89ue67VmxTqoJojTtk1XOlI6AWqQNXrQjdx1Y2HKhNbq/DA+cX5DfW/Dbo+9yDn5E8XcO06+TUwQS9Q7QlUFVB1TFWnINx4rrve6ez05KxqbWsVVHNP/rQN1y6TXwMT9ALVHnmqUrSHatsYYGbXCr2BTcyod7GBoIvk18AEvUC1p1BdgdMBVJ+4ah1Um5pRbxuubSe/BiboBao9hapt37+tqGEK/Jp8MCWAlY6EXmyhIaiuvbvdRfS+af868VRFeRWZwcp3E4CvR9n0A+8SrnQk9GILDUB1Pdlz+EGXoX5wc/ROzayHlKfuAqpmOevUHVVdQbVtuDad/BqYoHfwUDUz/T8+Gr1RUA0ppdIFVNvQ28WC+jbg2mTya2CC3sFDVXt8Kg65GkaPv71Un4eUp+4DVM1trKVCtS24NpX8Gpigd/BQ1d6qiknK2XQfqOYqUZ3jQtdxYfe2VXMSK3RCqasH3hZc6Ujo5R4kQnW7/POz5dnrF8uJ6mAnLyrLVvuWfG67tOzl62e/tf+L367D9v3Vtd17tlwsXlSXwnaUte66dG6TcKU0NoIklqiuiqleT071JKa6Wblg91L196aXHXIDS9r62RRcc40y8NDQO/jh/3roP/pgzviHlKcuMaZal8mqr1B1hV32OUcreoFq72KqoWWrS4WqzsN6HSOu2Koas560NOMsEazABL1ANZOU4qnKxNXVx3yxDKnE6guaLoyzCbi2vU4XvUAVqBY8/FfQNKFqpgi8/OerpU+KwNBr7NI4c8M1Js4KTNALVPcQqrawgJkiUOutSxEY6q2WYJxNwRWYoJd7AFSdKQJXta88UgSGXmdJxpkTrl2GP9ALVIFqQTfQlSLwX4uHS9/SKyHeaonGmQuuPuEAYIJeoLrnUPVJERhS26ruWks2ztxwBSboBapD9FQdKQIni/VEVWhtqzpvtQ/GmQOubeZoRS9QBaoF3UBbikA1cbXathpR26ruevtknKlwtYUDgAl6geqeQ9UJ2XvPljG1req81T4aZ06vFZigF6gODKp64urSWv0gLK66TyVKcnmtwAS9QHVgUNUTV1Kvq7bV/HTyjSuVoAusfTfOFLg2kZ8VSAFVoFq6p3o1caX01tW2qouv7iNUU+FK8mv0AtWBQdW3tpWazPpyPH0ZGgbYN+NMhSsdFKgC1T2Hqo9eDV6fYoJDqVAaA9ecYAVSQLWXUJVenAaKb/q/fYHq9bbWwEQrQ6lQGgpXkl8D1cFCVScdkTAJKVO9D1C11eoCqnnhSgcFqoOBqiqXYs5+h5RU6TNUt9ICBiZYMa9/aMYZAtc2kl9r56AudKMLWWq96xfq4S+u0dha7+EH+b2ZTtJM2GOeT1+/PNalw1W9GKj2qprq6MOD8cE7CZaQMtV9gqq63vsGDKrKb4fAZajG2TRYw6rqVr8clR3r73W2sluOHXbSoTC/l46I1Gm2t2rSs0qHzdEBqj2ppqoqpd46ebhcLDaVRyeL+oqqJVVTLUGoSPqPYK819/kXKzt+uKqca62aq767qhi8W3HXUY33t99MFsb3r58t79/87Vxbv5f/m9WKLZ976FicrPsilU57VE3V5oHqN2Sdp1oF1SG+7Zpa/N4378Q3JJA7+fVqxDX+9tI1lLet6tB6bcN76WWa35spJU3dWm9ViKBOh74mWXQTT7Unw38zdqrhOZSYam6wMjnhH2/Nmfxal9HRcDKHzrJysC9UZ+Pjl+p483tzqO6CalUIoU6HrV1AtS9QFQ8utkw1UG3OW+17R6qDa47k18pWHx+N3mhgroBV4xnWQVUdrwGXA6rm73yg6qsXqBYGVRngN3cZDW2daq7hL1CtnsyqgmtMW+WW440cf5ReaQhUzZ13UlbpIz2H/7Z2aufEZ/gPVHsM1RKHvX2G6lDjyqlbX2Ozf5kVHmxLq0I9VddozhZKMP+vgqqK+/roAKpAFaj+uJ2jFKjGwTU0+bVrY4qKYcrhdUxM1QVVrV8uh5IxXFd7Z+PDn3112M4LVIHqoKE6xH3vObe++uxUc23ckOEs7Z26Zv/N0IFtMrZ28b8891VlCXXe589Pjqt01208YfYfqAJVoJp162vuTRVmCKDJe1uXj9dHzBU3QBWoDvrB5ALr0DqSC6y51kGbO6py3wPlfZ7dS9+lx44qoApUgWpjW19zg1V5rHLvf2n3gb3/QBWoOvQOLe1d0+W0c+/cI5sUUAWqQHVwHQmoYgtAlQeT9d4A1ea8VeAHVIFqT6E6lATNXUCV5NdAFagO8MEA1XxgrQIuHR+oAtUBQbXprPdD7kixcAV+QBWo9lgvUG1ebyhcgR9QBao9h+q+D1FLLKcN/IBqZ1A1Fxz7pv0DqmHDVDpS83p9J7OAH1BtDKo6VZqGakh5aqAaBtXQe0VHypOoxXbvgR9QbQyqqmzE6Vd/utRQDSmlAlTD9ALVdvVKmJpwBX5AtRGoqmH+k+nFSA7/Q8pTA9VwqO7rDHWpbXWBFbsFqtmgupFXy7OTdTlfWYK6rjw1JaopZ93n8tk2++UeIVk81YvpZCSLmYV4qpSojtebuzwz3kmc12qDK3ZL342Gqqu4WWh5aob/cXqBand6bcmvySlA380WU7V5oyHlqYFqPFT3bYF6n9rquv854ApUgap1iM86VaA6hOflA1fslr4bBdXUtz5QjV+kTkfqVm/VcyCnAH0XqAJVOlKE3rpn0YecAltVZC3VWZvUayunvVUtVhRcBKpAtVG9QLUcvT7g9Dmmi/uwCteNv728/vvmwa++xQdz6FWT2TJUqHTK4oWy4CJQBaqNQ7W0Djr05+XjkVbBten2Ks/RXI0zn05H0hNcQczTO6xqr49e1Z7xbHa25am+fra8e3P0QZfpXnuyo3epZbuBKp00+f4B1XKzirlWCsS0d3uJ4+Gvp/Ppn1U+DtP7c0HVNmRX8Jsvnn621qP0Hn9UUNtMQq//D2mv1quhqmD55Xj6cmf4v3i4NeTX11fXbqAKVLNBdR8yKe1rApxQuKa0Vw2ZNYxm48Of5cqbEKjK1TxriB7+InU9nxx/r/5fD9vtm3hsw3VzlZDKG6LAbEJV7cKUvweqQLV1vUC1XL2+E1Q51rhKj1UCKAR+tsxyMqapzvF4/Ogn/b3vfTD1SrgDVaBadDYloFqe3hBQpsJVD89NAPl6qtp7NIGooSd/HwJrqde1I1O/DBj+A9Ui9ALVsvWGLqmKAav2Buez4290zDMEqsojrfru1uejDw+Ojv9t01sXTqgC4k5M1ZioWr8oNv8DVaDaGlT7nEiZGLhdry9czRlyGV/1gar6XMY7zePMZPS+96FOrxWqliVVvku8gCpQzaoXqPY7XFOltwquZix1M0O/WThfufRJeaE7Q/FtT1eJnqDyvQ++emsX/2dYowpU6aRZOitQ7dfIwkdvbLw1tb0Kck9OZ2fYAlAdnF6g2r+XYMwzC4VrantdYQNsAagOAqp9rKM05EQiKc+s6ZLaeobfNQTHFjJCdXtZxHachNR/3XdSoNovvSmL//etpPZgoSqD1nKmkRLV5Xg+dKR+Jr+O7RP7UlKb4f+P2+vIKKcCVHleaXpTy7LY4Iot9Ayqco0cJarLGU7SkfYz+XXOsAC2UABUrfL62XISUKKaksvtlVXmXvAMKafdkxLVUmanJ2c6bkqJ6rJidHgn+5/8OjSsUHo/G/zw39zXS0y1LKg2cX/pSGUmv/bVmxOu2EJmqEovVMVVn0zmX1OiuizjBKrDSn4dojcHXLGFjFDdTfu1WZPKOtWyoJr7HtORyk9+HQPrUkpqu3RuOXENFxR0HWcLZ7KjamBQbeIeA9X+JL8O0VtKSW1XmFHDs42CglXHye+A6oChyuTE/ultau9/1yW1TZ3mPE3TBQXN/K224+RcEVAdIFRz32eg2t/k1zFgbbu4pG07fGWS68wFBU19tuPkfBFQHTBUc91roNr/5Ne54Nq0Lfhk/c9dUNAc7tuOk7qB6kChmvNeA9X9SX6dGhJo2hZMr3HHS22goKAPVOVnQHXgUGVt4n7rbdqjbCOnQAhUmygo6DP8B6pANev9Bqr7m/w61XNtE6pNFRQ0P7cdB1SBalZvFajuf/LrLuHqE1NtuqBg3XHEVIFq1nsOVIeR/DqkvU1tfbUNvZsoKKirxW7lha4oPMjsP1DN6q0C1WElvw5pbxNbX+viqjnv7fx08k3VSgPpybJOFagC1YHrbXPLcu6tr1W7n3LcW+2ZVuV+toUGgCpQzXLfgeqwk1+HtDfn1lczjtrFvWXvP1BtLeMRz6s/etveCBKaM5lyKkC1l1BNufdAdT/0tr0SpOly2kAVqBYB1dLTvaG3Wb1dxNf3qZy2isWe3dukPz2dT/+sVhG40p4C1T2Hauz9B6okv87R3j6V067LqyAzZcldXnsF1Sb0NrUspUu9MeduamlOn/Q28cxKsIOQ8+da/9pGzbpUu61LKiPXtVbt8gKqA4BqzL0CqvsH1dhjm9gB1hRYc0HVtQV4vfvr8JeqaidWA22qDC+CIEgfRXFMZ8v6y1eH/2vb3dW6p4ogCNJfqL5aPj4avdEgVZsDXBsVskBVxRpmp//113UhwPUM2Zen07/qLWdNJnpg+N/csI/h/34O/0N+29bwP1cooInhv5z9V7HUTdFTe2HBLFBdUVspn1/8cR13ePqZCuhqkgPVcvQCVaAa8vs2oJo6mdbWRJWvnmSorsvI7q7X0jQPzUUY2pmGrreUekc8r/7rbbOcSp133ESZ7hQgtwpVW5VD7TLr5AUYfVmgAqroDfHWulxfXUI5baBakF5zXZvSu4nH2Hdj+I0MRPmIraUefnqloZrZeLSu+1excakr5Bym3u1dKdszp6n3BKjm19tmOZWccN0LqFYP/9fruVIudLsmzXZnXJdOiO+M5stBQyAL/HRCXDFDqGYQT48O3yp9ZjEzf53rhLy6TvlCL0oO1Kvup04EbMJP6Tp7vVlCcp3Q1/McNr3PJ8ffK50auFuJggPbXpWWzcwwlPIi0Hpti75T9ZovR9/2xvQH37aauuXMt+ucPrptbTaZ4PPcJFxd9yHXM+sUqludpIGJKtUZ9Q0wO+PZvS+WsYCyAXAD1TT4uTzAVVEyAVmZBNdHZCZydf1qicfiqoOG6tXGaRqz1qWfmdYVeo6q9GmyfEaMXhPYWq/5HFNfBHptovlyTNf7Ymm+HNW98NEb2h9C2mrTbXqJMS9Em95LWaMq8LlVtSnHMysCqrYlVePT+Vlul9zsjLdOXixjASVF7eM9/epPl9dQzQA/1c4H44N3slSDKp8rO1dV/ZyqN776zeoc428v9Z7kUL0uqOr/9TPT/4eeowqqEiQxbTeP0XrN55j6IjDrHZkvnmi9v3mU5ssx5gXj0x9iXrimbrmBJ+WFKPUuBBNin5uEq2xrjmfWOVTbinOYnfH+d6+WsYCSD/nJ9GIkf58Kv5V3Mh69m061J/LJR/UAU/XKIYx8M8eASYYA2oaqugb90s0FVdtzTG2zrsxpvhyT9V4Np+XLMUavT3+ItQ2p20x+nfJClGErV/8L1bu1SD/TMxsMVM3OmArVlZcwfvSTglNuqMrj9ZszB1QvppORTj2mh+kpUDWHpm1AdXZ6cqaHXnmg+mppe46pbVbPy/ZyTIfqJmYvJ3lD9fr0h1jbkLpdya9jdGu9OkFJjuemdUq42p6ZnOgCqnqYYHTGVKgqQOlYT06omkONa1BljqleTyglDG1MqDYdUzXruMe0fQdSi2dL23PMAVXbyzEHVM2XY0x7ffpDLFSlbtl/9edVL2Qfvfoe5Hhusq2rF6GAq35m5uoBoHp1E8zOmBJT3Z49FLGZDPCTs/QyQC4nwCQgY2LKEqryHKF6TWOTem0Q9z2HzWglpNQ9ejKZfx3Tdql7e6nW9nNMjn0adqC/zx1TvZ5ACdDr2x9iX1ryGDlqkZ+btuNzHzbVSeWKgvjnttNW8cyqtsEOPqYqjVJ2Rj3bGQOoqnOkwu/ayI0lMzmWasl66HKYHqPX1CU7S8o6VZteZcTbxr3REdp210SVDbgpLwI5Sy91Jeu9ivuZM/6+ekP6Q0pbtW4zxCTPKSewqnSbvz8TXnXsc7O3dfeZmVCN6dN7BdWqzljyOtUmwyC5dbpSnZU6YjGBnWOdqktv7HrSOr2uF1qd3pj+4NtWl+7FiWkf2y/EusX5Nr16zXLsc3O11XxmLil+nWoXMEHvMKGK3nL1hmwpbautuTJhAVWgGg1ToIreFL1V2a7abmvOFINAFagmgRU7QG+KXtOW+lL4D6iit7HhP3aA3hx6fWo+AVWMaC+havMusAP0AlWgClQzgRU7QG+q3rpYJlDFiAYBVdqK3hx6fauTDgqqCIIgTZar72Pbo6GKIAiCxAs3AUEQBKgiCIIAVQRBEKCK7K/I9Ie2irhSZAKQumN9RScRtukMaRsSL7JAZ92xuW1AJj6Rqf6S7apGr+uac9kchjVgkbV8VqXGHYat4PflePqyCaDrzE+r4m1GDk2ftiE54FOfiS23DcgyMjojVUw5pKp2ysz/Ptecy+YwroF0HjMhr0x4vTHAde2hnd+LDO052yS9AZnYO6RtSI7Rwvq+Vx6XaAOmDc6n05H0BFcQy+H9np/fkDpsyaht15zT5jCsPRi6q7euLs1hewPboGpCzfQc64ZEcuiu665vcmBu14Z3DSVd5/dtG9IOVF02kGqDNnucL55+lmJXOzZm8TZt15zT5jCsPRjCa2OYjQ9/tnUOm0GbBudjROvEwGbG/u3YlK7xvptEeCPqvOth2KaTyPPHtA1p1lN12UCKDZr2qIfeKXa18xLwhGpOm8Ow9shjlQZQZ3yxRmT+Tv4vq2N6xdREHE0aOlAtF6pVAAq1QdmG8dGjNzvhgAi7qrIxoIoEG4/LAFKG/7Zzyfo+0kDleXw6lFn2QreH4X/ZULXVeIqxQS2z8fFLc1ifYld1IQCG/0htp1Bv+fns+BtXzMlnosr8vxLgV7O20nBvfT768ODo+N+xk0lyQiG2bUh7UJU2EGuD2naqKqWm2pVZmdV1zTltDsPqfYfYzFDK2JaPQZtLSLzqwVtiZnrSKmZJjPYIzN/GtA1pB6rSBlJsUH0mn6t5TIpdXdvWVVVWn2vOZXMYVk/FjGNtZkj9Fy67Avr6c6Xn+fOTY63XjJlJ0RMJIR5E1RrJuskGJF/YyHy28vkrO6o7LsYG5UaCjex6uaF2ta1317Zc15LT5jAuJAvgn5zOzrgXCHYFVJEcQ8ia5TIIMiS74uEh0aJnYhmeI9gVUEUQBAGqCIIgQBVBEGRA8v+YesQk8EctxAAAAABJRU5ErkJggg==)
The coordinates of the corner points A(140,50),B(20,40) and C(40,100).
![](data:image/png;base64,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)
Now, we find the maximum value of Z. According to table the maximum value of Z = 595 at point A (140,50).
Hence, 140 and 50 be be the bags of brands P and Q respectively to be added to the garden to maximize the amount of nitrogen.
Question 10.A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?
Answer:let x and y be the number of dolls of type A and B respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Maximize Z = 12x + 16y ….(1)
Subject to the constraints,
x + y ≤ 1200 …..(2)
y ≤ x/2 ⇒ 2y ≤ x …..(3)
x – 3y ≤ 600 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
![](data:image/png;base64,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)
The coordinates of the corner points A(600,0), B(1050,150) and C(800,400).
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAgUAAABnCAIAAAAfXaYiAAAAAXNSR0IArs4c6QAAIVJJREFUeF7tndvrXdW1x4/n3UvTPIUQgtaHEEHRakSqkIKpRhDFa2ofBAVtAr6IqfVCH6zxghcQr6UBEW9pUxCxtlXQB0vRqMGCIQ+mIqHkqReNf0DPx/PljDOcc6255l577fXbe//GetjsvfaYY475HWOOMe/zhP/85z//FU8gEAgEAoHAqkfgv1c9AgFAIBAIBAKBwDcIRDwIOwgEAoFAIBCIeBA2EAgEAoFAIPB/CET/IGwhEAgEAoFA4BsETrD55BNOOCEgCQQCgUAgEFhVCPglRd+KB7HWaKHtgIgeGlxoDYbwgcDICCROI8aLRsY/sgsEAoFAYE4RiHgwp4oJsQKBQCAQGBmBiAcjAx7ZBQKBQCAwpwhEPJhTxYRYgUAgEAiMjEDEg5EBj+zmGoGHH36YGbY///nPcy3lt4WbH5lfffXV733vewDIw/cFwjBEFQITxIN//vOfzz333CWXXCJ98/CdN59//vmqQlNlry/y/FTX0GC91kQpa1+s8DBpGYeiB6UdO3b87W9/E8OjR4/mnFUX2p7BccbgyYtME0l4T7gyV7ZmzZrrr7/+r3/961BQTMmnTWxji/AIbDAOKHltPCDLLVu23HrrrX/6059MLL7z5rTTTpuy/JF8BARCgyOAvJqzePnllyn+e++9x6Jnnt27d68sGhj8rl27GmU4fPgwoctc2b///e99+/Zt3bp1Hpq2BbEpC6GCSIDwCGxF+/rrr4eCuioeIMRVV11F5P/+97//+9//XvrmQfd33XXXaosHKvtQChiHT2iwH85//OMf0fUPfvCDfslXVSqcKf6hjBVBwryHfXnllVcA6qc//emAONN2Puuss7zTTHRBdriyf/zjH4ghz0ZU2Lt374Aqa+yalPl3iv3YY49RKFyuCT+wfZpWEDRXld48++yz/PujH/2ojcDeIyXIqsxJ8JAPhQnoowzREFF4+PLQQw9Z2u985zsQSFU+9lx33XXGGRvyf4kDrOAvmkZRLS+SS87GvGpK4XEj008++cTE4ws/RWDymB0gJ+8pHV8slELmS9SJcyPBimswx1+6BmRko7AU2avV/wsNuFnrEkqSoAhDScmTgnsMPeyQVdqV1zUcpC8TQz8tU/2kCFao3Mj5l0aSL3K57hhPXzSkIhX1Ti8RzExFQJmB8a+wSqCzn+KQywBBW4VqM79CvUjcXI2vUC4KBsCY1Pd+VcDXyqTGlRnKWkxsQZrYm7xWAmyBbc6hs1AextzaNRaHJbRhJVuCzGekorW5l8Rp/L+tF7xJYzZ52aTa5PFyqDCqKnosHviX+otKZVk0crbaogJbHFLyRuhFmedFxSjnlZTCm3sjQ4QRw7Z4kL8v4N9pRlbn2yhH0GCOPz6rADU2nf+bVMicwJROSa1VYeYEvTnKNl132pXM0qvPUBWMiVT8tBpIoRIcJFvBP8q2fbkUAHhp1T6rVd/IYJn2iAflCtVoReXanUhYGQ9kIYMHA5Pf2gSdNSinTFoGjWoqswWT3Kd3SgJBm9hSdKHhKCGTTLElQG4LIYnbqYoHpMGPl0ui2EXGNqCEcPz0oshoGttxKoZMHDiUUDnKcXjOmBE2ZASCz3NoE9V8BNXP8lIFlh+pLEUSD3yh1Pc0hvBMqitvyEtJpCQ+Aa2yChW0UIgoI2vQO1Ogtl65PLigVqfTbBfcMBgIlFaggSQvldzMSQTWrhQ39be8582tos2urIIhgxxxOR5Yn0AdBe/NJQNMZF3SrJeqUX3yifYXqUhiUORJlIuFkEnjQWeFynOsqRdJX6rT8SkY+MBmSUx3qtf5U9lIr48H0rtvWRtKfJGovtXYWToIvHnX0CfFz2OJEEbv1ubIO83I6X21FFewpcRp1MaDTm+l6p3ELtpivLQIoRqeQNOoM6nH13w/b8F7VTOZhTj4dl8b+o15iZXQryxFEg8ScMSk0H+XkoAi6dlNZDQ5caJaT9DpkurL3qbBBH+VMXkpTyeobdS4seWSB1GSyJwEbF6Beal6IoaVdpU0zJN8G8eLPLAK7VZ1qYp5d74TfJXLejaJ/SiuAJcNZ8k/WqaTxgMhX6hQuWnV1IuJ4oE6Ur4/5zMdOR4IkLzdbYNIiNqjEzOjeJBHR+9/EpebmFan06iaT0aCI0eO5HL4N1999RU/169f719eeuml/Pz000/t5Xe/+90yH/179tlnG5kWrl122WV+mRo/Ez4nn3xyDeec5qSTTrKXlaUoZ7R58+YywamnnkrE/uijj/Ad55577s6dO1lAxpRvP/krU81agwn+x44dQ7A9e/Z4ra1du9akvfjii6ljzzzzDC9Z+Xf33Xe/+eab5bL4LL788kuIQdInueaaa/jJ6pE2PrlddSqrLNKZZ57pCYiCLMCvNHJLeNNNN/Gdpdt68+tf/xrDsMlV5mlZ2qclJX51X6Xec7LKCuUTDlIvjCGmjsax/xdffDEBUDSUvdw2GnDmGcMDW4IB63YSrMiFWAvmqBWldKrVr8XXkvSf/exn3v7zla89lGg9ZjWLialIaEtOZUtPPPEEn+BM/aKWNYLcmHVVPCD+gMg8LMZKyvCXv/ylB6DzkOTpp5+m9UH0xsjQGRaJMc0uJMyVBt955x1UQME//PBDjRFRcCIHMZ7QOA/aGVkGohoK0gYuKjaO8o477jAZHnnkEQ1kUfnVh+hsPveWf5wKde+991JGVL99+/beok6fEKvD3jC8xmDg+bP0aPrshuJA3LLIBIB33nknnK2hIFviJ+767bffRvLbb7+9PuuqeHDllVfCsVxX1Xb7+9//7vP+wx/+wM8zzjijXqCcUpyT7q2aD4OscZbMGzZs4HN2pcjLRevj/vvv14pGAgM1pNCwnQZA0o6vwRNPPJF8GwfxKLIVB+MmNBIYGEDAjgmNhZJ+8cUX/Ltu3To+TznlFD6TNspvf/tbXm7atKkGLun6+PHjNcT1NP2C+o033kjVJST85je/Ia+rr77aclQZ+YvKX9/QKwjco0INWC9wI2gZw8jb4yYzG9MK29YG2SFI3KUFBqqE2DZJEIMGvlaLsTuhU7Oqy/ZQnGQOYEp/dc4558Czcdee3JcebIlP1s4++uijSF7AOTeSqniAddKBJeYwuOE79UhGJ5cOMnzp/vOJso2Av4i9CERvt7465ZTifNttt8FZKuGT7+TVb0PjwYMHzY9gEPBBSOUyu1L4lhdiCygrTu/Brkpgx9cgnguboeb7HewUnO65Bkb45LtpkBEJuXj/AJpBRF8bbsQMjRFdccUVfNJqVk9ZbT1iKgSd/Xplcf7558uuJIP2rD744IOVkDaSIQ8yUDSJjWyVPR4MDyN87bXXKCMdprwIBhRm8+STTxaEVPMLGskAPY7P0/eoUEPVCxBWAWkJTYPzlGnBBP8Ok88++6wtxILe5ZdfzmALor7++utE6xtuuGHKfKdMfu2118IBqczH8kUWe9555xlzAgC2BM6YYr4Gr0MGH80KY3aNaweNtRLWrDfN56Ub5/00RWbyNHKGwM8n1yztauto+6mkSUuBGEmhlIvNJyeZImejGD0mrBJ9ecRyVY6sQQRoy1GakoqTJ1lflPybTD/WrDdNrCKxK1uAbxmRhddd53wyBYHectH0sn/EsHM5Bnz8phyvPq13yHm2zSfnC3lzGcoVqtEPdNaLmvnksjOqXDVUnlrQv40ZWcJG21MSk0HT3cmi3honU+gfdEpeFlsDCTlNPhNuZJ0rVhKnUdU/IA1RlFgKHH7hPN+1mlAiEpfyHSsT9VbazAUm6EkLaUXDd1DoN61EWr8TB5m9kIOXQrNS2k+E/PTsGNAAN0OSv/AFdDYrG7blStX27/gaJEe1UGwvFXWMgmvKiy4LVut3L4ISY0defk+Ayt59913fmoPYgJVJJASdQD311FO2d0xrWzUa2/tBPAzVCiWR4PbDH/6wk+ctt9wCjZ9JVhKGiRBMGGp9IdOwBW5YEZnaVgmtXEjoe1SowetFJyArSEDPVdPdtmCBoR4gZfio35jEUGWhs4IxeAPD3nIfqypmnekJcq/sH3RGtoUgqF+PvBDFmah/sFglalxvulhFkLTJgtRFLELI3A8BvPBE/Yl+uRQ6c4Wda21uv7Z/MEGECdJAIBD4XwSYP7j55pvVUgtIVhsC+NwpJ5B7I/b8889POpOsvCIe9MY8EgYCDQj4hTEcqaYp7kHWBQXcgUANArRCWPvTb+Qz4kENwkETCNQigPe3WS4N9/v1tbVcgi4Q6IuA1u/5Jcv1nE6wufiJ7nipzyAoA4FAIBAIBOYWAb8c61vxoG2d1tyWJATzCBDRQ4NhEoFAIFCPQOI0YryoHrqgDAQCgUBgmRGIeLDM2o2yBQKBQCBQj0DEg3qsgjIQCAQCgWVGIOLBMms3yhYIBAKBQD0CI8UDnQyuE33n/GH17po1azikr/M4wzkvSIgXCAQCgcBECEwWD/CV2m4z0cUOrIdlfwQH1yTnbOBw+YszU8UTL5yIzul99m9ytKoodaolCZWc7zVOvJyKrUMc/8I5ULt27ZoIynkmTm7q8Hum7DwWHcZJINS/AN6oZV4aDQq1izis+LzhvZhAOZGpzDOGIVsgsPwITHR+kY7N06WAladt6LTF/HxH3YGc4Ot5Np6n6G9BaLy7PL/NMZGzMtUinp8DmG1KKZyXkNwVnGgkucCg8UhRf4Zi45mmNVeZVppTkAUCgcCACCROo+r+ZMueMIDD7byT04vb5lgVDPBTbYfcapOnXW+rG1x9HNIbu4XYLrIvn+JUmaotjA2oicFZFeJBY17aSWvXF+PrASe5xReeRqCj2Ugildlt8v62bh0cyxu7xFh67Dx3d3A0gmEgEAh0ItA/HugcdrkM1fnOzCDAHeRtdrX98R1tHHQQaZKFfI05LLV5k8ZpmS3Z1adS2FsgRzZRPKg56lVYWcBWaE/CLfrl8b3MpO+oAJxcW19jOUETCAQCs0YgcRoTzB+88cYbJOZYDEbYcfE1k8MMJXOvkI549A/H7/GT29OS9/ZTt4lddNFFnkCXodulksxJ4Hr8jeo6NSw/7d0zqU916aWXkpA7SNuEXOj3XKqHH9c56eXHLpnQvcf+Jib9RMW6b05TEdu2bfMMdWF9Ps3QlW38HwgEAmMjUBsPdJsgLXTd2YKLxwv4uzMbBX///fd5r4sJc6e8f/9+P3uZc1u/fr1PdcEFF/Dz6NGj9lJXdfpHF8eXUaxMJT+4lI4MVYISJyAWbuDRKYn5hIEPwOCjm16OHTtmmG/cuNHjLxiTi47HNvPILxAIBCoQqI0HNJMJALq0lkf3qb7wwgvlLLgUF4LGw37xR1w2ZL6bRv1ll102b2tR6AYtpSO75557yp0Dwj8hn+Lfd999FVYUJIFAILAMCNTGA12woDDAQyORlvi+fftq1nc24sRQjy0WYu5Ro8xT3mY+uEJmeoHl4NJWMiToEoa5bLKtdPQMtmzZArdZX+FZKXCQBQKBwDgIVMUD2sgMHdA/WLt2rS1d5w0i9h5eZ9CGi2FVSBwTl8cSYMjCX096/Phxj4ImFbh/2F7m0UjTA2Xs+qUaRx+zzoWyE3SBqO1ea/DfunUrsb8tGCToaVJh3bp1Jrk6hfZIocko06yLGfwDgUCgBwJV8aDg9B999NEeuTIQceDAgca+hTyLpgo0g23PwYMH+c5l9HpD/GCUyY/naKw/39bgmUyUqnfvpwcm4yTZu3cvQfeXv/xlY3Z0HS688EJCxYcffpj3HjRVkBgDeiR4yN1rqoBeo2d+6NAhfsYFYePoN3IJBKZCoGY/Gs1Jv6bQkmgBaGFFpkaBbIWoJbRNAPrLxov8UsVB9h/AWeiYkJX7DyQqCSuX1c56WVgNf6Qtk2m2pm0voVaXFnZvxP6DGi0ETSCwQAgkTqN7P5q8QOMWU+1IKOw+VdrGted5K54A4CPHIPuTJaHf6FC5PxmNaoX+Ai2c74wHWizUtgGwrVnh95bH/uQFquohaiDQicDE8aC8GxknXj67onE/mvoE7G/SWD80OJq8n4E3t7DBF39YhcqpLbLqSYiJbaYVgYRPEnam8mmXZj+aOgf5wSG+g9gYEpIkpjUF2rzzxxt1HNUXgb7TKIMgEAgEVgSBJB7M/L5MhqRZV0qb1LY1tbVDZ/GeQ9kYLj9y5MikzJk5OP3009lstUCXocd9mZNqOegDgVWOwNj3ZbIDlpZ72wTmTJWBT2fC+Y477uiRi+ZdWaffI20kCQQCgUBgERGoWl80TcFYpvLAAw+wDJSjrafh0yPtBx98QCoO2Jg0LeuU6NMw6LEifZpJpQ36QCAQCAQGQeBb40WDcAwmgUAgEAgEAouCgBZS6pn5/MGigLIEcsb8wRIoMYoQCIyJwNjzB2OWLfIKBAKBQCAQ6I3AzOcPeksWCQOBQCAQCATGRCDiwZhoR16BQCAQCMwvAhEP5lc3IVkgEAgEAmMiMFI8uOSSS5i4qLlSbczCr2xeO3fuBJPxl+GubKkj90AgEJhbBKriAUcW2zHX9oVTMDvvR1OxcXnsP+AgoMYzltlCTLRoBAj+/Ksc+ZJnl0vFm4RbJ5OCbkgLQ38EtxFPnzU3ELDF4dZbbx35Cra7774b4fNSN2oZyuSSIn7arXYoNBeeN7wXPlDmdxyxT5BYuGbNGgj45PvynSM7txU+BAsESgj442vaDtDQyW6NT9vhaMaKw4LYn9x4bA4n6uiK9sZ/O8+z88tmvWyeWw2TtlLb6UmNZWxEY9KsC+D0OMwEkcqpyA5AdNxTTtmmZX8A0fTn2dWfJ9gDgUgSCAQCEyGQuILu803hLk/h/QKuXK6h87Qyefzcpep0ZT2N8aDzvGvFg8IBbRDUMOn0jG3xYJCs2/CZSKkiLscDZWRPW6kLCh3kvOuJzhvvAUIkCQQCgXoEhokHFiQ6j4NuO9+0HA8UgZK7B3Rqpj9QsxwPKpnMIh7UZ60bGga5ZWHW8UARJbkgAf36uzEgSM67VQAwO5He/amxCjP+TPJ6aw7KQCAQmAaBxGlUzR/4dqW+cysZR9RxBnX5dCCGkjkVjpvZcw6cG2qt2vxfXY150UUX+b/OPvtsfh4+fDinb3zTmwnHFkm2pE1dmS9k9VlzvhMucoSZ9t27d6tQPhLXlwhKXY3Jma8+FT9RsW6p00TLtm3bPMHmzZv5adMMutDUX5+pq9M4eXAiYYI4EAgEBkdggnjAEW82iUqVpmLffvvt5Rvn33//fSQ+//zz+8m9fv16n1CXaB49etS/RAxJpZnJfHqzhkk/8YbKmnsozaX2k2TAVKZlpoKZec5nepObkHWJ5rFjx0yGjRs3enl0JqC/1hTOicCEKF3PEE8gEAisIAITxINcyh07drQtDRKxrlYf5+5cXOozzzzDXfAjL9ehgFNmfcYZZyQudQUNwrLGQe/Zswf9xuKfeVBHyBAIjIDABPEgmWlk2JfxItrII4x1tAHhB850LReumeO1RwBuwKxPOumkEQTuzMJGyVQ0La9iGGf//v2daYMgEAgElgCBCeJBUlpa/Y8//jgvX3vttRkBcfz4cc9Zg/IbNmxozA55FJm+/PJLTzARk34FWcGs+wlck2r79u3Srzp59iTdBU0qrFu3zggSek0q+FGmvMOhSYUaqYImEAgEZodA/3gwO5ngrKmCN954w+dy8OBBfm7atKkt68TR9GPSr1zTZJ1ErH4CzCJVIpimCt5++22f14EDB1hfJHevqYJ9+/Z5gkOHDvHTxgyZKqDP4acTNL5nF2XPoiDBMxAIBKoQsHEPqNvWLeX7D2w8gVTJAkTPRGsN8yvXPQ0E/fYfMDp01113GXONX8HNj2vV7D+ACakaV3y2bQ4YKmu/iskvwey3gKygQc9Q64vyLGihoy8Tg/EioWfbL2L/QT+9RKpAYG4RSFzBBPvRGsNLedm4PEjjHoXGVY9+51fn1uJGDoQEVvQb+p1MoFQU8UGrcaeuD1pDZW0LQP0S/t6mU44HjWtnfexs1G8SJmN/cm/tRMJAYA4RGCwe4BMLPQMrec1+NPNEyU5gOzFC4wn8TGZxadrbOAPNW7ybDwZ+XlRZ5Ey0HYz3nnNnPCB4TJ+1clyp/WgCxMcD4MXd2zg+mDTqlyRGQ2sg7/xpYl/8pZSkGlBkMlLng0++51qbw5oTIgUCy4dAn3gwDQoDnscwjRhtaXGCIFIT2GaROzwHxKdyvGhGBQm2gUAgsHAIJE5j5vcnM9F6+umns4uVDcmNIxIr+5ItV+xa+Ne//rUiYgwLTtyfvCJKjEwDgcVFYOz7k9nAzIYAFhTO50H/b731Vj4mPpp2d+3axYaJ3qdijCZnZBQIBAKrAYGZ9w8EIttcCQkMyzRegbAagM7LyOkadE2YbL/lllsGQSD6B4PAGEwCgdWDQOI0vhUPVg8KUdJAIBAIBAIBzR8YDiP1DwL3ERCI/sEIIEcWgcAyITD2/MEyYRdlCQQCgUBgiRGY0/MqlhjxKFogEAgEAvOJQMSD+dRLSBUIBAKBwNgIRDwYG/HILxAIBAKB+URgpHjw8MMPM3HBCsv5RGFwqdhodu6551Lk8S/nGbwswTAQCARWCQITxAN8HHvK2Elgt2bynTf+7OJG1PCJ3MLImTZPP/20JyCtnCYPX4gZSXISsl9BBFyymBNAz0v+Eg3Ek/pfrkwgYX7L25RZswuP/dic3nPVVVfN2/1ibMmmyG32jTYh8JAmlJ2Ad0IHILQMuN/UbjkdDSIuY5Cp5Jc42V+NZtbPHaiy6AaIeAKBBUDADtxA1sLhGxxSVrixpHxqByffcWxZcmZZ465gf5omOerIM/9wipzPq/O4zbJgdvppcuD2UFk3nhM+uxNOyhrU2XkUWag2imFnXBvmCTKdgHdChwz5VQfJeYKzg8hOKsSYk1xkpRQ8P4Cvtzw6Bzc5pbE3t0gYCAyOQOIKqs67pg4rGCTng2LoOOi8anmhG32izsEmoVUV80R2XqbOyLTDL6FUdbUD+muO4y9HOLjp8oPE6w2YdWMsHFypYliOB8mpGLkMACuE/a0SnqwG8E7odCUGhiQ98qnwMM6RgrJGuWmfo1npsPFgRooOtoHAUAj0iQeqw4231nSKJQeRdA4ag0Ry0qcChucvMew2BdEnfgSPVnOXgJqx6o7kRRsw6zHPT50yHqjt33hZhbRQA3gndPLF/vIfhZnyRRqdZlZJYIaHGN66+MmTmyVSWbcYg/Hne2PSMjZv27IrqynJ1UOyNEzCzgPnC1Dw2AHgZOfPdW+sKdOzrYQryJYegT7xIK/D9TCpFiX0qkvWSNS/voqqGiSXsSQvG6WqEVUNYZMqiQeDZz2asyvHA1NB2/1ouStPtNYJeA10jbl0Zl1vb2VKc6/6osaEAhJvcufL++TBciyYWW9DmWooDIduESJ33DnDxmHYJItkCGt6tkPhGXwWHYHEaVTNJ+u6c38lem7WjW+YWuT8zq1btyb/Mt367rvv8hdsNSnNVPCRI0d+97vfecqNGzf6n7qeN5m+TqTSHb/Hjh1rk5CpSzX6nnrqqUIpBsya2suNwZWIrRSZ5jxxZzbT2zY/3wl4J3RMVifFBCI84DRlR61Mg9dzwJbI9J577iEJ5sd3WVfyJLUdv4zR2g3SJOENtUNT0Pfeey+KxoYx74Ik1smgyNihPtUn0E1BpE0uqa4p14zY1mQdNEuDQFU8oLR5Ha6B4Ouvv4Zs8+bNjcTwxIhPOeWUn//851zCvm3bthNPPLGGbW8avIaWErH4p1xpe2eRJzznnHOmdHYDClNmhRY4chWXJzJ+nnXWWQuxPAZtIvZEC5oJBugFV06RFRjyB4NhJRKNFa0UYpkcNF999ZVR7t69m1jCe12kQYfjzDPPLIAMMQxFQ2TVwBEtoe3bt/OFUvz4xz9OsqjR/ozY1mQdNMuEQG08wGQHLDZtfDoNtOWpGzxcR0NF4ioC2qedq1enEePw4cO04HjWrl1rq2ZhSBOPnwMuNPRCnnzyydPIPGZa3IrN52tQm9yffPLJMWXondd9992HCeG7K1evqouAK2/rHGCKW7Zs2bFjB3ERC2kT7KWXXmIQac+ePcA16XHuso3BI+6M2PZWTSRcFASq4oG68wN66r1799Kau+mmmwwmKtITTzzBy/3799tL3xCzapOMVySV/5133oFy3bp1UypgBbOeUvJpkhOhrXkLztovgjf0PDsB74Qu99cakGyTXJsZOx9iPFaKtPlukjbO6ha0dQ4eeeQRGNKEZzBHYbLxYm1jvlK37E2j8UgbCHgEquLBlVdeSZqJOuNllD/++GMIaK23kWkwN/FEhw4d4qU5LE0VJCOtBw4coLHWNtUB23z+ByZaEELfn++DZ534x/m0v02bNiGYomnymKfuBLwGOs2m+LaFthDmmxJMDPRSM2unRQo00utvZpU9NM4ckLuEpP/KYE5hFOiGG26AjEW6mOuMupjzaTMh1fIhUBUPrr76apwCjTh2Eb/55puGAv1c5uIKUwuaD5Af948CzI033mjc+PKLX/yClxs2bBClluIRhNScJC+mGfhy8cUXi0CrLCBQd1u7XulhJH12bYHO96MWdDlU1sqC4Fdo/M6JSTFyTalRMRjKD/KpFgDzOvWAd0In1UNmudx88828ueKKK6aEgstH6dDwDDszZIM5mGg+dEYAALQXX3zx/vvv1+jTsIM/itO/+tWvBBexE6UUBq+mxDCSr3YErOUFEIVWWOO+U8OukLBtvWlje9CvTO3c6UqmndtlaTMiZHlHgkKLL8IgWXtgx1lcX9Zg4y3NfiGj7UfzVQI1+fX1nYB3Qjej/ckIX7OvuLxjPPlXe0f8k2xgFoHtmc93JDRuFPCWluy5sSEpXxYxycXwBpYYcA3bmi5X0Cw9AonTqOofkIb+8meffYadeevkO9uX5HPbHlqX9KOTIWMd7wM3azjjd2DlW/HkyJpU27kDJfS0wnxGNAY9E4hJ4geLPvjgA+gbz8YoyDxI1uKvDtD0jd8Rmi3gxkiO3xgFtslCrE7AO6GT6i2XSUd42nBAeA33DfgwTMQyB5mozI9+gPGnwf6Tn/wEuzWbpGivv/46PVSNIA31MF9tBoyFE7TOO++8oZgHn0DAIzDz+zLpPl944YXUpcGra40iWQXIwg8ajz02T9Tw76RhbpMpDULpsIMYjfkyLEZzplOkIAgEAoFAQAgkTmPm8YAsx/SJiZqZPKBlN9HkwYCGMnIsjHgwoO6CVSCwGhBYgXjAJBjbmujqjuyXGaRiDSKDvNrsM/JD7qxeJ1PGrEboHOShfuTyRnaBQCCwcAiU4sHCFSYEDgQCgUAgEJgGAT/IHCPO0yAZaQOBQCAQWB4EatcXLU+JoySBQCAQCAQCTQhEPAi7CAQCgUAgEPgGgf8B2bxjNs1DltYAAAAASUVORK5CYII=)
Now, we find the maximum value of Z. According to table the maximum value of Z = 16000 at point C (800,400).
Hence, 800 and 400 be the number of dolls of type A and B respectively.
Refer to Example 9. How many packets of each food should be used to maximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?
Answer:
let x and y be the number of packets of food P and Q respectively. Obviously, x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Maximize Z = 6x + 3y ….(1)
Subject to the constraints,
12x + 3y ≥ 240 (constraint on calcium) i.e. 4x + y ≥ 80 …..(2)
4x + 20y ≥ 460 (constraint on iron) i.e. x + 5y ≥ 115 …..(3)
6x + 4y ≤ 300 (constraint on cholesterol) i.e. 3x + 2y ≤ 150 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
The coordinates of the corner points A(15,20),B(40,15), and C(2,72).
Now, we find the maximum value of Z. According to table the maximum value of Z = 285 at point B (40,15).
Hence, to get the maximum amount of vitamin A in the diet, the packets of food P should be 40 and the packets of food Q should be 15. The maximum amount of vitamin A will be 285.
Question 2.
A farmer mixes two brands P and Q of cattle feed. Brand P, costing Rs 250 per bag, contains 3 units of nutritional element A, 2.5 units of element B and 2 units of element C. Brand Q costing Rs 200 per bag contains 1.5 units of nutritional element A, 11.25 units of element B, and 3 units of element C. The minimum requirements of nutrients A, B and C are 18 units, 45 units and 24 units respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag?
Answer:
let x and y be the amount of two bands P and Q respectively which are mixed. Obviously, x ≥ 0, y ≥ 0.
The given information can be formulated in a table as:
Mathematical formulation of given problem is as follows:
Maximize Z = 250x + 200y ….(1)
Subject to the constraints,
3x + 1.5y ≥ 18 …..(2)
2.5x + 11.25y ≥ 45 …..(3)
2x + 3y ≥ 24 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5).
The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is unbounded.
The coordinates of the corner points A(18,0), B(9,2), C(3,6) and D(0,12).
As, feasible region is unbounded so 1950 may or may not be minimum value of Z.
So, 1950 is the minimum value of Z, if the open half plane is determined by 250x + 200y <1950 has no point in common with the feasible region. Otherwise z has no minimum value.
For this we will draw the graph of inequality 250x + 200y <1950 or 5x + 4y < 39. Here we find that 250x + 200y <1950 has no point in common with the feasible region. Hence the minimum value of Z is 1950 at C(3,6).
So, 3 and 6 be the amount of two bands P and Q respectively which are mixed to get minimum cost to Rs 1950.
Question 3.
A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg food is given below:
One kg of food X costs Rs 16 and one kg of food Y costs Rs 20. Find the least cost of the mixture which will produce the required diet?
Answer:
let x kg and y kg be amount of food X and Y respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Minimize Z = 16x + 20y ….(1)
Subject to the constraints,
x + 2y ≥ 10 …..(2)
x + y ≥ 6 …..(3)
3x + y ≥ 8 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is unbounded.
The coordinates of the corner points A(10,0),B(2,4), C(1,5)and D(0,8).
As, feasible region is unbounded so 112 may or may not be minimum value of Z.
So, 112 is the minimum value of Z, if the open half plane is determined by 16x + 20y <112 has no point in common with the feasible region. Otherwise z has no minimum value.
For this we will draw the graph of inequality 16x + 20y <112 or 4x + 5y<28. Here we find that 16x + 20y <112 has no point in common with the feasible region. Hence the minimum value of Z is 112 at B(2,4).
So, 2kg and 4kg be the amount of two foods P and Q respectively which are mixed to get minimum cost to Rs 112.
Question 4.
A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:
Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.
Answer:
let x and y be the number of toys manufactured per day of type A and B respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Maximize Z = 7.5x + 5y ….(1)
Subject to the constraints,
2x + y ≤ 60 …..(2)
x ≤ 60 …..(3)
2x + 3y ≤ 120 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
The coordinates of the corner points A(20,0),B(20,20), C(15,30)and D(0,40).
Now, we find the maximum value of Z. According to table the maximum value of Z = 262.5 at point C (15,30).
Hence, 15 and 20 be the number of toys manufactured per day of type A and B respectively to get the maximum profit.
Question 5.
An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. What is the maximum profit?
Answer:
let x and y be the number of tickets of executive class and economy class respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Maximize Z = 1000x + 600y ….(1)
Subject to the constraints,
x + y ≤ 200 …..(2)
x ≥ 20 …..(3)
y - 4x ≥ 0 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
The coordinates of the corner points A(20,80),B(40,160) and C(20,180).
Now, we find the maximum value of Z. According to table the maximum value of Z = 136000 at point B (40,160).
Hence, 40 and 160 be the number of tickets of executive class and economy class respectively to get the maximum profit.
Question 6.
Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively. They supply to 3 ration shops, D, E and F whose requirements are 60, 50 and 40 quintals respectively. The cost of transportation per quintal from the godowns to the shops are given in the following table:
How should the supplies be transported in order that the transportation cost is minimum? What is the minimum cost?
Answer:
let x and y quintal of grain supplied by A to shop d and E respectively. Then 100 - x - y will be supplied to shop F. Obviously x ≥ 0, y ≥ 0.
Since requirement at shop D is 60 quintal but supplied x quintal hence, 60 - x is sent form B to D.
Similarly requirement at shop E is 50 quintal but supplied y quintal hence, 50 - y is sent form B to E.
Similarly requirement at shop E is 40 quintal but supplied 100 - x - y quintal hence, 40 - (100 - x - y) i.e. x + y - 60 is sent form B to E.
Diagrammatically it can be explained as:
As x ≥ 0, y ≥ 0 and 100 - x - y ≥ 0 ⇒ x + y ≤ 100
60 - x ≥ 0, 50 - y ≥ 0 and x + y - 60 ≥ 0
⇒ x ≤ 60, y ≤ 50 and x + y ≥ 60
Total transportation cost Z can be calculated as:
Z = 6x + 3y + 2.5(100 - x - y) + 4(60 - x) + 2(50 - y) + 3(x + y - 60)
= 6x + 3y + 250 - 2.5x - 2.5y + 240 - 4x + 100 - 2y + 3x + 3y - 180
Z = 2.5x + 1.5y + 410
Mathematical formulation of given problem is as follows:
Minimize Z = 2.5x + 1.5y + 410 ….(1)
Subject to the constraints,
x + y ≤ 100 …..(2)
x ≤ 60 …..(3)
y ≤ 50 ….(4)
x + y ≥ 60 …(5)
x ≥ 0, y ≥ 0 ….(6)
Now let us graph the feasible region of the system of inequalities (2) to (6). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
The coordinates of the corner points A(60,0),B(60,40),C(50,50) and D(10,50).
Now, we find the minimum value of Z. According to table the minimum value of Z = 510 at point D (10,50).
Hence, the amount of grain delivered from A to D, E and F is 10 quintal, 50 quintals and 40 quintals respectively and from B to D,E and F is 50 quintal, 0 quintal and 0 quintal respectively.
Question 7.
An oil company has two depots A and B with capacities of 7000 L and 4000 L respectively. The company is to supply oil to three petrol pumps, D, E and F whose requirements are 4500L, 3000L and 3500L respectively. The distances (in km) between the depots and the petrol pumps is given in the following table:
Assuming that the transportation cost of 10 liters of oil is Re 1 per km, how should the delivery be scheduled in order that the transportation cost is minimum? What is the minimum cost?
Answer:
let x and y liters of oil be supplied by A to shop D and E respectively. Then 7000 - x - y will be supplied to F. Obviously x ≥ 0, y ≥ 0.
Since requirement at D is 4500L but supplied x quintal hence, 4500 - x is sent form B to D.
Similarly requirement at E is 3000L but supplied y quintal hence, 3000 - y is sent form B to E.
Similarly requirement at E is 3500 quintal but supplied 7000 - x - y quintal hence, 3500 - (7000 - x - y) i.e. x + y - 3500 is sent form B to E.
Diagrammatically it can be explained as:
As x ≥ 0, y ≥ 0 and 7000 - x - y ≥ 0 ⇒ x + y ≤ 7000
4500 - x ≥ 0, 3000 - y ≥ 0 and x + y - 3500 ≥ 0
⇒ x ≤ 4500, y ≤ 3000 and x + y ≥ 3500
Cost of delivering 10L of petrol = Re.1
Then Cost of delivering 1L of petrol = Rs.1/10
Total transportation cost Z can be calculated as:
Z =
Z = 0.3x + 0.1y + 3950
Mathematical formulation of given problem is as follows:
Minimize Z = 0.3x + 0.1y + 3950 ….(1)
Subject to the constraints,
x + y ≤ 7000 …..(2)
x ≤ 4500 …..(3)
y ≤ 3000 ….(4)
x + y ≥ 3500 …(5)
x ≥ 0, y ≥ 0 ….(6)
Now let us graph the feasible region of the system of inequalities (2) to (6). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
The coordinates of the corner points A(3500,0),B(4500,0),C(4500,2500), D(4000,3000) and E(500,3000) .
Now, we find the minimum value of Z. According to table the minimum value of Z = 4400 at point E (500,3000).
Hence, the amount of oil delivered from A to D, E and F is 500L, 3000L and 3500L quintals respectively and from B to D,E and F is 4000L, 0 L and 0 L respectively.
Question 8.
A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine.
If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden?
Answer:
let x and y be the bags of brands P and Q respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Minimize Z = 3x + 3.5y ….(1)
Subject to the constraints,
x + 2y ≤ 240 …..(2)
3x + 1.5y ≤ 270 ⇒ x + 0.5y=90 …..(3)
1.5x + 2y ≤ 310 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
The coordinates of the corner points A(140,50),B(20,40) and C(40,100).
Now, we find the minimum value of Z. According to table the minimum value of Z = 470 at point C (40,100).
Hence, 40 and 100 be be the bags of brands P and Q respectively to be added to the garden to minimize the amount of nitrogen.
Question 9.
Refer to Question 8. If the grower wants to maximise the amount of nitrogen added to the garden, how many bags of each brand should be added? What is the maximum amount of nitrogen added?
Answer:
let x and y be the bags of brands P and Q respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Maximize Z = 3x + 3.5y ….(1)
Subject to the constraints,
x + 2y ≤ 240 …..(2)
3x + 1.5y ≤ 270 ⇒ x + 0.5y=90 …..(3)
1.5x + 2y ≤ 310 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
The coordinates of the corner points A(140,50),B(20,40) and C(40,100).
Now, we find the maximum value of Z. According to table the maximum value of Z = 595 at point A (140,50).
Hence, 140 and 50 be be the bags of brands P and Q respectively to be added to the garden to maximize the amount of nitrogen.
Question 10.
A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?
Answer:
let x and y be the number of dolls of type A and B respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:
Maximize Z = 12x + 16y ….(1)
Subject to the constraints,
x + y ≤ 1200 …..(2)
y ≤ x/2 ⇒ 2y ≤ x …..(3)
x – 3y ≤ 600 ….(4)
x ≥ 0, y ≥ 0 ….(5)
Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.
The coordinates of the corner points A(600,0), B(1050,150) and C(800,400).
Now, we find the maximum value of Z. According to table the maximum value of Z = 16000 at point C (800,400).
Hence, 800 and 400 be the number of dolls of type A and B respectively.