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Question

The corner points of the feasible region determined by the system of linear constraints are (0,10),(5,5),(25,20) and (0,30). Let Z=px+qy, where p,q>0. Condition on p and q so that the maximum of Z occurs at both the points (25,20) and (0,30) is

A
5p=2q
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B
2p=5q
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C
p=2q
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D
q=3p
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Solution

The correct option is A 5p=2q
Maximum Z=px+qy occurs at points (25,20) and (0,30).
Hence, 25p+20q=30q
25p=10q
5p=2q

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