Given the following linear optimization problem

Maximize $40$x $+20$y

Subject to

x$+$ y$320$

$3$x $+$ y $480$

$2$x $+$ y$160$

x$,$ y $0$

$$Graph the constraints and determine the feasible region for this problem.

$$Find the coordinates of each corner point of the feasible region for this problem.

$$Determine the optimal solution and optimal objective function value for this problem.