Formulate the LP problem and solve graphically using the Objective Function Line Method.

JAM, Inc. is a small manufacturer of sports and school bags. Its distributor believes that a market exists for both medium-priced school bags, Product A, and high-priced sports bags, Product B. The distributor is so confident of the market that, if JAM can make the bags at a competitive price, the distributor will purchase all the bags that it can manufacture over the next three months. A careful analysis of the manufacturing requirements resulted in the following table, which shows the production time requirements for the four required manufacturing operations and the accounting departments estimate of the profit contribution per bag:

The director of manufacturing estimates that 630 hours of cutting and dyeing time, 600 hours of sewing time, 708 hours of finishing time, and 135 hours of inspection and packaging time will be available for the production of sports and school bags during the next three months. How many bags of each model should it manufacture?

Graph Feasible Region and show optimal solution

Production time in hours Product Cutting and dyeing Sewing Finishing Inspection and Packaging Profit per bag Product A 7/10 1/2 1 1/10 P200 Product B 1 5/6 2/3 14 P180 Production time in hours Product Cutting and dyeing Sewing Finishing Inspection and Packaging Profit per bag Product A 7/10 1/2 1 1/10 P200 Product B 1 5/6 2/3 14 P180