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 . The relation between p and q , so that the maximum z occurs at both points (15, 15) and (0, 20) is

Step-by-step solution

The value of the objective function z = px + qy at the given corner points is calculated as follows: At (15, 15) , z = 15p + 15q At (0, 20) , z = 0p + 20q = 20q Since the maximum value of z occurs at both (15, 15) and (0, 20) , the values of z at these points must be equal. 15p + 15q = 20q 15p = 5q q = 3p Answer: q = 3p