The corner points of the feasible region determined by a system of linear constraints are $(0,3), (1,1)$ and $(3,0)$. Let $Z = px + qy$, where $p, q > 0$. The condition on $p$ and $q$ such that the minimum of $Z$ occurs at both $(3,0)$ and $(1,1)$ is $.....$

• A
  $p = 2q$
• B
  $p = \frac{q}{2}$
• C
  $p = 3q$
• D
  $p = q$