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