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Question
The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is ______.
Options
p = q
p = 2q
q = 2p
q = 3p
Solution
The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is q = 3p.
Explanation:
Since Z occurs maximum at (15, 15) and (0, 20)
Therefore, 15p + 15q = 0.p + 20q
⇒ q = 3p.
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