The corner points of the feasible region for an LPP are (0, 10), (5, 5), (15, 15) and (0, 20). If the objective function is $z=px +qy, q > 0 $ then the condition so that the maximum of Z occurs at (15, 15) and (0, 20) is :

$q=3p$

The correct answer is Option (4) → $q=3p$

The objective function is,

$Z=px+qy,q>0$

$Z(15,15)=Z(0,20)$

$⇒15p+15q=20q$

$⇒q=3p$