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Question
A linear programming problem is given by Z = px + qy where p, q > 0 subject to the constraints: x + y ≤ 60, 5x + y ≤ 100, x ≥ 0 and y ≥ 0
- Solve graphically to find the corner points of the feasible region.
- If Z = px + qy is maximum at (0, 60) and (10, 50), find the relation of p and q. Also mention the number of optimal solution(s) in this case.
Solution
i. From graph, corner points are: A(0, 60), B(10, 50), C(20, 0), D(0, 0)
ii. Z = px + qy
Given, Z is maximum at (0, 60) and (10, 50)
∴ 0.p + 60.q = 10.p + 50.q
`\implies` 10p = 10q
`\implies` p = q
So there can be infinite number of optimal solutions.
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