Answer
minimum at $(2,0)$ with $z=4$.
Work Step by Step
Graph the given inequalities as shown
$\begin{cases}x\ge0 \\ y\ge0 \\ x+y\ge2 \\ x\le5 \\ y\le3 \end{cases}$
We can identify the corner points $\left(2,0\right),\left(0,2\right),\left(0,3\right),\left(5,0\right),\left(5,3\right)$ which give the values $z=2x+5y=4,10,15,10,25$. We can find the minimum at $(2,0)$ with $z=4$.
