For the objective function $z=px +qy $, where p, q > 0 the corner points of the feasible region determined by the system of linear constraints are - (0, 10), (5, 5), (15, 15) and (0, 20), condition on p and q so that maximum of z occurs at both the points (15, 15) and (0, 20) is :

$q=3p$

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

As maximum occurs at (15, 15) as well as (0, 20)

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

$⇒15p+15q=20q$

$15p=5q$

$3p=q$