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Q.

The corner 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 $Z = p x + q y, p, q > 0$ , 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

$q = 2 p$

b

$p = 2 q$

c

$p = q$

d

$q = 3 p$

answer is D.

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Detailed Solution

Given,

The L.P.P.'s feasible region's corner points $= (0, 10), (5, 5), (15, 15)$ $(0, 20)$

Objective function $Z = p x + q y, p, q > 0$

Since, Z occurs maximum at the points $(15, 15)$ and $(0, 20)$ .

So,

$15 p + 15 q = 0 \cdot p + 20 q$

$q = 3 p$

This is the required relation.

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The corner 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