Sanderson Manufacturing produces ornate, decorative wood frame doors and windows. Each item produced goes through 3 manufacturing processes: cutting, sanding, and finishing. Each door produced requires 1 hour in cutting, 30 minutes in sanding, and 30 minutes in finishing. Each window requires 30 minutes in cutting, 45 minutes in sanding, and 1 hour in finishing. In the coming week Sanderson has 40 hours of cutting capacity available, 40 hours of sanding capacity, and 60 hours of finishing capacity. Assume that all doors produced can be sold for a profit of $500 and all windows can be sold for a profit of $400.

a. Formulate an LP model for this problem.

b. Sketch the feasible region.

c. What is the optimal solution?