Bowie furniture assemble three-types of recliners made from three types of imported lumber, Mahogany (M) and Cherry (C). The time it takes to identify parts, assemble, ship Mahogany recliner is 20, 50, and 24 minutes respectively. Similarly, the time it takes to identify parts and assemble a Cherry recliner is 30 minutes each. Cherry recliners are picked up from the plant by customers. The total available time in the three departments are 40, 30, and 20 hours, respectively. Bowie furniture earns $20.00 profit per Mahogany and $22.00 per Cherry recliner;
1. Set up the linear programming problem.
2. Graph the constraints and shade the feasible area.
3. Solve the problem graphically and determine the maximum profit?
4. Find the upper and lower limit for unit profit of Mahogany (M) given a unit profit of Cherry (C=$22).