Corner points of the feasible region determined by the system of linear constraints are $(0,3),(1,1)$ and $(3,0).$

Question

Let Z=px+qy,where p,q>0.Condition on p and q so that the minimum of Z occurs at (3,0) and (1,1) is

$$(A)\;p=2q\quad(B)\;p=\frac{q}{2}\quad(C)\;p=3q\quad(D)\;p=q$$