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Question
Solve the following linear programming problem graphically:
Maximize Z = 10500x + 9000y
Subject to Constraint
x + y ≤ 50
2x + y ≤ 80
x, y ≥ 0
Chart
Graph
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Solution
Maximize Z = 10500x + 9000y
Subject to Constraint:
x + y ≤ 50 ...(1)
2x + y ≤ 80 ...(2)
x, y ≥ 0
By using (1)
x + y = 50
| x | 0 | 50 |
| y | 50 | 0 |
By using (2) 2x + y = 80
| x | 0 | 40 |
| y | 80 | 0 |
| Corner points | Z = 10500x + 9000y |
| A (0, 50) | 4,50,000 |
| B (0, 0) | 0 |
| C (40, 0) | 4,20,000 |
| D (30, 20) | 4,95,000 → max. |
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