Answer
maximum at $(2,6)$ with $z=28$.
Work Step by Step
Graph the given inequalities as shown
$\begin{cases}x\ge0 \\ y\ge0 \\ x+y\ge2 \\ x+y\le8 \\ 2x+y\le10 \end{cases}$
We can identify the corner points $\left(2,0\right),\left(0,2\right),\left(0,8\right),\left(5,0\right),\left(2,6\right)$ which give the values $z=5x+3y=10,6,24,25,28$. We can find the maximum at $(2,6)$ with $z=28$.
