AAI ATC Junior Executive 27 Dec 2023 Shift 2 Paper

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.
What is the condition on p and q so that the minimum of Z occurs at (3, 0) and (1, 1)?