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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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p = q

q = 2p

p = 2q

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)

$\begin{array}{l} \Rightarrow p \times 15 + q \times 15 = p \times 0 + q \times 20 \\ \Rightarrow 15 p + 15 q = 20 q \Rightarrow 15 p = 5 q \\ \Rightarrow q = 3 p \end{array}$

$∴$ Option (d) is the correct answer.

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