The value of objective function is maximum under linear constraints

The corner points of the feasible region determined by the following system of linear inequalities: $2x+y\le 10,x+3y\le 15,x,y\ge 0\text{ are }(0,0),(5,0),(3,4)$and $(0,5).$ Let $Z=px+q{y}_{\text{'}}$ where $p, q>0.$ Condition on $p$ and $q$ so that the maximum of $Z$ occurs at both $(3, 4)$ and $(0,5)$