Answer
minimum at $(0,2)$ with $z=8$.
Work Step by Step
Graph the given inequalities as shown
$\begin{cases}x\ge0 \\ y\ge0 \\ 2x+3y\ge6 \\ x+y\le8 \end{cases}$
We can identify the corner points $\left(3,0\right),\left(0,2\right),\left(0,8\right),\left(8,0\right)$ which give the values $z=3x+4y=9,8,32,24$. We can find the minimum at $(0,2)$ with $z=8$.
