Problem:

A leather company manufactures leather jackets and leather handbags. A leather jacket requires 8 square feet of leather, while a handbag requires 2 square feet. In addition, a lining fabric is required, 6 square feet being used for a leather jacket and 1 square foot for a hand bag. Each leather jacket requires 12 hours of labour time, and each handbag 5 hours. Each week, there are 1200 square feet of leather, 800 square feet of lining fabric and 1840 hours of labour time available. The profit on a leather jacket is $350 and on a handbag $120.

(a) Formulate the problem of maximizing weekly profit as a linear programming problem.

(b) Answer the LP problem to determine the optimal solution.

(c) Do any of the constraints have slack or surplus? If yes, which one(s) and how much slack or surplus does each have?