Question

The corner points of the feasible region determined by the system of linear constraints are $(0,10),(5,5),(25,20)$ and $(0,30)$. Let $Z=px+qy$, where $p,q>0$. Condition on $p$ and $q$ so that the maximum of $Z$ occurs at both the points $(25,20)$ and $(0,30)$ is

• A. $5p=2q$
• B. $2p=5q$
• C. $p=2q$
• D. $q=3p$

Answer 1

The correct option is A $5p=2q$

Maximum $Z=px+qy$ occurs at points $(25,20)$ and $(0,30)$.
Hence, $25p+20q=30q$
$\Rightarrow 25p=10q$
$\Rightarrow 5p=2q$