Answer
maximum $z=64$ at $(0,8)$.
Work Step by Step
1. See graph for the inequalities
$\begin{cases}x\ge0 \\2x+y\le8 \\ x-3y\le3 \end{cases}$
2. It is bounded with corners $\left(0,-1\right),\left(0,8\right),\left(\frac{27}{7},\frac{2}{7}\right)$
3. Evaluate $z=5x+8y$ at corner points to get $z=-8, 64, 21.6$, thus we have the maximum $z=64$ at $(0,8)$.
