Linear Programming Question - CBSE

Question

The corner points of the feasible region determined by system of linear constraints are $(0, 10), (5, 5), (15, 15), (0, 20)$. Let $Z = p x + q y$ where $p, q > 0$. Condition on $p$ and $q$ so that maximum of $Z$ occurs at both $(15, 15)$ and $(0, 20)$ is:
(a) $q = 3p$
(b) $p = q$
(c) $p = 2q$
(d) $q = 2p$

Accepted Answer

Z(15,15) = 15p + 15q, Z(0,20) = 20q. Equating gives 15p + 15q = 20q \implies 5q = 15p \implies q = 3p. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Selecting $q = 3p$: 1.0 Mark

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