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Question
Solve the following LPP graphically:
Maximise Z = 2x + 3y, subject to x + y ≤ 4, x ≥ 0, y ≥ 0
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Solution
The shaded region (OAB) in the Figure is the feasible region determined by the system of constraints x ≥ 0, y ≥ 0 and x + y ≤ 4.
The feasible region OAB is bounded
So, maximum value will occur at a corner point of the feasible region.
Corner Points are O(0, 0), A (4, 0) and B (0, 4)
Evaluate Z at each of these corner point.
| Corner Point | Value of Z | |
| 0,(0, 0) | 2 (0) + 3 (0) = 0 | |
| A(4, 0) | 2 (4) + 3 (0) = 8 | |
| B(0, 4) | 2 (0) + 3 (4) = 12 | ← Maximum |
Hence, the maximum value of Z is 12 at the point (0, 4)
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