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Question
Solve graphically:
Maximise Z = 2x + y subject to
x + y ≤ 1200
x + y ≥ 600
`y ≤ x/2`
x ≥ 0, y ≥ 0
Graph
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Solution
x + y ≤ 1200
| x | 1200 | 0 |
| y | 0 | 1200 |
x + y ≥ 600
| x | 600 | 0 |
| y | 0 | 200 |
`y ≤ x/2`
| x | 400 | 0 |
| y | 200 | 0 |
| Corner points | Value of Z = 2x + y |
| A(600, 0) | 1200 |
| B(1200, 0) | 2400 → Maximum |
| C(800, 400) | 2000 |
| D(400, 200) | 1000 |
Hence, Z is maximum for x = 1200, y = 0
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