Answer
maximum at $(6,0)$ with $z=12$.
Work Step by Step
Graph the given inequalities as shown
$\begin{cases}x\ge0 \\ y\ge0 \\ x+y\le6 \\ x+y\ge1 \end{cases}$
We can identify the corner points $\left(1,0\right),\left(0,1\right),\left(0,6\right),\left(6,0\right)$ which give the values $z=2x+y=2,1,6,12$. We can find the maximum at $(6,0)$ with $z=12$.
