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Question
Determine the minimum value of Z = 3x + 2y (if any), if the feasible region for an LPP is shown in Figue.
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Solution
The feasible region (R) is unbounded. Therefore minimum of Z may or may not exist. If it exists, it will be at the corner point (Figure)
| Corner Point | Value of Z | |
| A,(12, 0) | 3(12) + 2(0) = 36 | |
| B(4, 2) | 3(4) + 2(2) = 16 | |
| C(1, 5) | 3(1) + 2(5) = 13 | ← (Smallest) |
| D(0, 10) | 3(0) + 2(10) = 20 |
Let us graph 3x + 2y < 13.
We see that the open half-plane determined by 3x + 2y < 13 and R do not have a common point.
So, the smallest value 13 is the minimum value of Z.
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