Answer
maximum $z=32$ at $(0,8)$.
Work Step by Step
1. See graph for $\begin{cases}x\ge0\\y\ge0\\3x+2y\ge6\\ x+y\le8 \end{cases}$
2. Identify the corner(s) as $\left(2,0\right),\left(8,0\right),\left(0,3\right),\left(0,8\right)$
3. Evaluate the expression $z=3x+4y$ at the above corners as $z=6,24,12,32$
4. Thus the maximum is $z=32$ at $(0,8)$.
