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Question
In figure, the feasible region (shaded) for a LPP is shown. Determine the maximum and minimum value of Z = x + 2y.
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Solution
Here, corner points are given as follows:
`"R"(7/2, 3/4)`
`"Q"(3/2, 15/4)`
`"P"(3/13, 24/13)`
And `"S"(18/7, 2/7)`
Now, evaluating the value of Z for the feasible region RQPS.
| Corner points | Value of Z = x + 2y | |
| `"R"(7/2, 3/4)` | Z = `7/2 + 2(3/4) = 5` | ← Maximum |
| `"Q"(3/2, 15/4)` | Z = `3/2 + 2(15/4) = 9` | |
| `"P"(3/13, 24/13)` | Z = `3/13 + 2(24/13) = 51/13` | |
| `"S"(18/7, 2/7)` | Z = `18/7 + 2(2/7) = 22/7` | ← Minimum |
Hence, the maximum value of Z is 9 at `(3/2, 15/4)` and the minimum value of Z is `22/7` at `(18/7, 2/7)`
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