The corner points of the feasible region determined by the following system of linear inequalities $ 2 x+y \leq 10, x+3 y \leq 15, x, y \geq 0 $ are $ (0,0),(5,0),(3,4) $ and $ (0,5) $. Let $ Z=p x+q y $, where $ p, q0 $. Condition on $ p $ and $ q $, so that the maximum of $ Z $ occurs at both $ (3,4) $ and $ (0,5) $, is

Question

The corner points of the feasible region determined by the following system of linear inequalities $ 2 x+y \leq 10, x+3 y \leq 15, x, y \geq 0 $ are $ (0,0),(5,0),(3,4) $ and $ (0,5) $. Let $ Z=p x+q y $, where $ p, q>0 $. Condition on $ p $ and $ q $, so that the maximum of $ Z $ occurs at both $ (3,4) $ and $ (0,5) $, is

YESPYQ · Accepted Answer

Correct answer: d) $ q=3 p $. As the maximum of $ Z $ occurs at both $ (3,4) $ and $ (0,5) $ $∴{Z}_{\left(3,4\right)}={Z}_{\left(0,5\right)}\ \Rightarrow 3p+4q=5q\ \Rightarrow 3p=q\ \Rightarrow q=3p$

The corner points of the feasible region determined by the following system of linear inequalities \( 2 x+y \leq 10, x+3…

Practice more JEE Maths PYQs