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 $z=px+qy$ 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. $q=3p$
• B. $p=2q$
• C. $q=2p$
• D. $p=q$

Answer 1

The correct option is A $q=3p$

$z=px+qy$

$z(15,15)=15p+15q$
$z(0,20)=20q$
Maximum of $z$ occurs at both the points $(15,15)$ and $(0,20)$
Hence, $15p+15q=20q$
$\Rightarrow q=3p$