Graph the system of inequalities and list each corner point. $$\left\{ \begin{array}{r@{}r@{}r} -13 y & \ge & -234 \cr -4 x - 4 y & \ge & -124 \cr -14 x+ 8 y & \ge & -126 \cr x & \ge & 0 \cr y & \ge & 0 \end{array} \right.$$
Corner Points:
If there is more than one corner point, type the points separated by a comma i.e.: (1,2),(3,4).

Determine the maximum value of $z=-3 x+ 2 y$ subject to the given system of linear inequality constraints