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

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=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 (A) q=3 p (B) p=2 q (C) q=2 p (D) p=q

Tardigrade Admin · Accepted Answer

z=p x+q y z(0,10)=10 q z(5,5)=5 p+5 q z(15,15)=15 p+15 q z(0,20)=20 q maxi. at (15,15) and (0,20) ∴ 15 p+15 q=20 q ⇒ 15 p=5 q ⇒ 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 $z = p x + q y$ 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

$q = 3 p$

$p = 2 q$

$q = 2 p$

$p = q$

$z = p x + q y$
$z (0, 10) = 10 q$
$z (5, 5) = 5 p + 5 q$
$z (15, 15) = 15 p + 15 q$
$z (0, 20) = 20 q$
maxi. at $(15, 15)$ and $(0, 20)$
$∴ 15 p + 15 q = 20 q$
$\Rightarrow 15 p = 5 q$
$\Rightarrow q = 3 p$

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

q=3p

p=2q

q=2p

p=q