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; p, q >0, then the condition on p and q so that the maximum of Z occurs at (15, 15) and (0, 20) is :

q=3p

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

maximum of Z occurs at both (15, 15) and (0, 20)

$⇒Z(15, 15)=Z(0, 20)$

$15p+15q=20q$

so $15p=5q⇒q=3p$