Question

The corner point of the feasible region determined by the system of Iinear constraints are $(0,10)$,$(5,5),(15,15)$ and $(0,20)$.Let $Z=px+qy,$ where $p,q>0$.Find the condition on $p$ and $q$ so that the maximum of $Z$ occurs at both the points $(15,15)$ and $(0,20)$.

Answer 1

Given $Z=px+qy$

$Z$ is maximum at both points

$⟹Z$ at $(15,15)$ is equal to $Z$ at $(0,20)$

$⟹15p+15q=20q⟹3p=q$