Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px+qy, where p, q 0. Condition on p and q so that the minimum of Z occurs at (3, 0) and (1, 1) is

Question

Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px+qy, where p, q > 0. Condition on p and q so that the minimum of Z occurs at (3, 0) and (1, 1) is

Philoid · Accepted Answer

Z = px + qy

Given, minimum occours at (3, 0) and (1, 1).

For minimum to occur at two points the value of Z at both points should be same.

So, value of Z at (3, 0) = value of Z at (1, 1)

⇒ 3p = p + q

⇒ 2p = q

So, option B is correct.