Answer
maximum at $(0,4)$ with $z=20$.
Work Step by Step
Graph the given inequalities as shown
$\begin{cases}x\ge0 \\ y\ge0 \\ x+y\ge2 \\ 2x+3y\le12 \\ 3x+2y\le12 \end{cases}$
We can identify the corner points $\left(2,0\right),\left(0,2\right),\left(0,4\right),\left(4,0\right),\left(2.4,2.4\right)$ which give the values $z=3x+5y=6,10,20,12,19.2$. We can find the maximum at $(0,4)$ with $z=20$.
