a) Let $\mathcal{R}$ be the region consisting of the points $(x,y)$ that satisfy \[-6 \le 3x - 5y \le 6\]and \[-3 \le x + 2y \le 3.\]Plot the region $\mathcal{R},$ and identify the vertices of polygon $\mathcal{R}.$ (
b) Find the maximum value of $x + y$ among all points $(x,y) \in \mathcal{R}.$
