Answer
maximum at $(5,7)$ with $z=26$.
Work Step by Step
Graph the given inequalities as shown
$\begin{cases}x\ge0 \\ y\ge0 \\ x+y\ge3 \\ x\le5 \\ y\le7 \end{cases}$
We can identify the corner points $\left(3,0\right),\left(0,3\right),\left(5,0\right),\left(0,7\right),\left(5,7\right)$ which give the values $z=x+3y=3,9,5,21,26$. We can find the maximum at $(5,7)$ with $z=26$.
