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Q.

The comer points of the feasible region for an L.P.P. are (0, 10), (5, 5) (15, 15) and (0, 20). If the objective function is Z = px + qy, p, q > 0, then the condition on p and q so that the maximum of Z occurs at (15, 15) and (0, 20) is

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a

p = q

b

q = 2p

c

p = 2q

d

q = 3p

answer is D.

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Detailed Solution

Z=px+qy,p,q>0

∵ Maximum of Z occurs at (15, 15) and (0, 20)

⇒p×15+q×15=p×0+q×20⇒15p+15q=20q⇒15p=5q⇒q=3p

∴ Option (d) is the correct answer.

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