Given the following linear optimization problem

Maximize 60x + 90y

Subject to
x + y ≤ 120
3x + y ≤ 180
x + y ≥ 40
x, y ≥ 0

(a) Graph the constraints and determine the feasible region.

(b) Find the coordinates of each corner point of the feasible region.

(c) Determine the optimal solution and optimal objective function value.