The corner points of the feasible region associated with the LPP: Maximise $Z = px + qy, p, q>0$ subject to $2x + y ≤ 10, x + 3y ≤15,x,y≥ 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). If optimum value occurs at both (3, 4) and (0, 5), then

$q = 3p$

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

Given objective function

$Z=px+qy,\;\;p,q>0$

Since optimum occurs at both $(3,4)$ and $(0,5)$,

$Z(3,4)=Z(0,5)$

$3p+4q=0\cdot p+5q$

$3p+4q=5q$

$3p=q$

Hence the required relation is $q=3p$.