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Question
Solve the following Linear Programming Problem graphically:
Minimize: z = x + 2y,
Subject to the constraints: x + 2y ≥ 100, 2x – y ≤ 0, 2x + y ≤ 200, x, y ≥ 0.
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Solution
The feasible region determined by the constraints, x + 2y ≥ 100, 2x – y ≤ 0, 2x + y ≤ 200, x, y ≥ 0, is given below.
A (0, 50), B (20, 40), C (50, 100) and D (0, 200) are the corner points of the feasible region.
The values of Z at these corner points are given below.
| Corner point | Corresponding value of Z = x + 2y |
|
| A (0, 50) | 100 | Minimum |
| B (20, 40) | 100 | Minimum |
| C (50, 100) | 250 | |
| D (0, 200) | 400 |
The minimum value of Z is 100 at all the points on the line segment joining the points (0, 50) and (20, 40).
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