The corner points of the feasible region determined by the system of linear constraints are $\left(0, 10\right), \left(5, 5\right), \left(15, 15\right), \left(0, 20\right)$. Let $z=px+qy$, where $p, q>0$. Condition on $p$ and $q$, so that the maximum of $z$ occurs at both the points $\left(15, 15\right)$ and $\left(0, 20\right)$ is