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
Answer & explanation
Correct answer: option 4
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 $q=3p$.