Chapter 8.6, Problem 34E

Consider the objective function $z=Ax+By(A>0\text{and}B\text{>0})$ subject to the following constraints: $2x+3y\le 9.x-y\le 2.x\ge 0$, and $y\ge 0$. Prove that the objective function will have the same maximum value at the vertices (3,1) and (0,3) if $A=\frac{2}{3}B$.