Consider the objective function $z = 4 x + 7 y$ subject to the following constraints: $$\left\{ \begin{array}{r@{}r@{}r} x + y & \ge & 2 \cr 2 x+ 3 y & \le & 12 \cr 3 x+ 2 y & \le & 12 \cr x & \ge & 0 \cr y & \ge & 0 \end{array} \right.$$
Find the feasible region and list the corner points.
Corner points:
If there is more than one corner point, type the points separated by a comma (i.e. (1,2),(3,4)).

Find the maximum and minimum values of $z$.
Maximum value of $z$ is: when $x =$ and $y =$
Minimum value of $z$ is: when $x =$ and $y =$