Question

The corner points of the feasible region determined by the 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 the maximum of $z$ occurs at both the points $(15,15)$ and $(0,20)$ is

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

Answer 1

Answer: (A)

$z=p x+q y$
$z(0,10)=10 q$
$z(5,5)=5 p+5 q$
$z(15,15)=15 p+15 q$
$z(0,20)=20 q$
maxi. at $(15,15)$ and $(0,20)$
$\therefore 15 p+15 q=20 q$
$\Rightarrow 15 p=5 q$
$\Rightarrow q=3 p$