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Question
Solve the following Linear Programming Problem graphically:
Maximize Z = 400x + 300y subject to x + y ≤ 200, x ≤ 40, x ≥ 20, y ≥ 0
Solution
We have Z= 400x + 300y subject to x + y ≤ 200, x ≤ 40, x ≥ 20, y ≥ 0
The corner points of the feasible region are C(20, 0), D(40, 0), B(40, 160), A(20, 180)
| Corner Point | Z = 400x + 300y |
| C(20, 0) | 8000 |
| D(40, 0) | 16000 |
| B(40, 160) | 64000 |
| A(20, 180) | 62000 |
Maximum profit occurs at x = 40, y = 160 and the maximum profit = ₹ 64,000
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