A maker of medical protective equipment produces three types of masks (small, medium and large) that are assembled from cloth, a metal nose strip and elastic cord. The small mask uses 13 square inches of cloth, 1 metal nose strip and 7 inches of elastic cord. The medium mask uses 15 square inches of cloth, 1 metal nose strip and 8 inches of elastic cord. The large mask uses 18 square inches of cloth, 1 metal nose strip and 10 inches of elastic cord. The profits for the three masks are: $0.10 per mask for small, $0.12 per mask for medium, and $0.15 per mask for large. For the next month, the mask maker has available 15,000 square inches of cloth, 1200 metal nose clips, and 10,000 inches of elastic cord. The demand for large masks is limited, so they should not produce more than 300 large masks in the next month. Required:
a. Formulate this as a linear programming problem to maximize the mask maker’s profit (suppose fractional masks are allowed and that all masks will be sold). Use Solver in Excel to find the optimal solution.
b. In the optimal solution, how many masks of each type should be made and what is the optimal profit?
c. In the optimal solution, how many masks of each type should be made and what is the optimal profit?