The corner points of the feasible region determined by the system of linear constraints are (0,3),(1,1) and (3,0) . If objective function is Z=p x+q y, p, q>0 then the condition on p and q so that the minimum of Z occurs at (3,0) and (1,1) is

Step-by-step solution

The objective function is Z = px + qy . The values of Z at the corner points are: At (0, 3) , Z = p(0) + q(3) = 3q . At (1, 1) , Z = p(1) + q(1) = p + q . At (3, 0) , Z = p(3) + q(0) = 3p . For the minimum of Z to occur at both (3, 0) and (1, 1) , the values of Z at these two points must be equal, and this value must be less than or equal to the value at the third corner point (0, 3) . Equating the values at (3, 0) and (1, 1) : 3p = p + q 2p = q p = q 2 Checking the condition at (0, 3) with q = 2p : Z(3, 0) = 3p Z(