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, $p, q> 0.$ Condition on p and q so that minimum of Z occurs at (3, 0) and (1, 1) is :

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

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