The corner points of the feasible region determined by a system of linear constraints are (0, 3), (1, 1) and (3, 0) . If the objective function is z = px + qy , where p, q > 0 , then the condition on p and q such that the minimum of z occurs at both (3, 0) and (1, 1) is _____

Step-by-step solution

The objective function is z = px + qy . The value of z at the corner point (3, 0) is z = 3p + 0 = 3p . The value of z at the corner point (1, 1) is z = p + q . Since the minimum of z occurs at both (3, 0) and (1, 1) , the values of z at these points must be equal. 3p = p + q 2p = q p = q 2 Checking the value at (0, 3) , z = 3q = 6p . Since p > 0 , 3p Answer: p = q 2