The corner points of the feasible region determined by the system of linear constraints are (0,10), (5,5), (15, 15), (0, 20). Let Z = px + qy, where p, q 0. Condition on p and q so that the maximum of Z occurs at both the points (15,15) and (0,20) is

Question

The corner points of the feasible region determined by the system of linear constraints are (0,10), (5,5), (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15,15) and (0,20) is (A) p = q  (B)  p = 2q  (C) q= 2p (D) q = 3p

Tardigrade Admin · Accepted Answer

Value of Z = px + qy at (15,15) is 15p + 15q and that at (0, 20) is 20 q. According to given condition, we must have 15p + 15 q = 20 q ⇒ 15p = 5q ⇒ q = 3p

Q. The corner points of the feasible region determined by the system of linear constraints are $(0, 10), (5, 5), (15, 15), (0, 20)$ . Let $Z = p x + q y$ , where $p, q > 0$ . Condition on $p$ and $q$ so that the maximum of $Z$ occurs at both the points $(15, 15)$ and $(0, 20)$ is

$p = q$

$p = 2 q$

$q = 2 p$

$q = 3 p$

Value of $Z = p x + q y$ at $(15, 15)$ is $15 p + 15 q$ and
that at $(0, 20)$ is $20 q$ .
According to given condition, we must have
$15 p + 15 q = 20 q$
$\Rightarrow 15 p = 5 q$
$\Rightarrow q = 3 p$

Q. The corner points of the feasible region determined by the system of linear constraints are (0,10),(5,5),(15,15),(0,20). Let Z=px+qy, where p,q>0. Condition on p and q so that the maximum of Z occurs at both the points (15,15) and (0,20) is

p=q

p=2q

q=2p

q=3p