The corner points of the feasible region determined by a set of constraints (linear inequalities) are $P(0,5)$, $Q(3,5), R(5,0)$ and $S(4,1)$ and the objective function is $Z=a x+2 b y$ where $a, b>0$. The condition on $a$ and $b$ such that the maximum $Z$ occurs at $Q$ and $S$ is