The corner points of the feasible region determined by the system of Linear Constraints are (0, 3), (1, 2) and (3, 0). Let $z=px+qy, $ where $p, q>0,$ be the objective function. Find the condition on p and q so that the minimum of z occurs at (3, 0) and (1, 2) :

$p=2q$ $p=3q$ $p=q$ $p=\frac{q}{2}$

$p=q$