In an LPP, corner points of the feasible region determined by the system of linear constraints are $(1, 1)$, $(3, 0)$ and $(0, 3)$. If $Z = ax + by$, where $a, b > 0$ is to be minimized, the condition on $a$ and $b$, so that the minimum of $Z$ occurs at $(3, 0)$ and $(1, 1)$, will be : (A) $a = 2b$ (B) $a = \frac{b}{2}$ (C) $a = 3b$ (D) $a = b$