Duke Manufacturing produces both baseballs and cricket balls on a weekly basis. The resources needed to produce baseballs and cricket balls are leather, cutting, and dyeing time, as well as sewing and packaging time. Each baseball requires 0.5 square feet of leather, and each cricket ball requires 0.4 square feet of leather. The cutting and dyeing time and the sewing and packaging time for each product and its profit contribution per unit are given in the following table:

Each week a total of 400 hours of cutting and dyeing time and 480 hours of sewing and packaging time are available. In addition, the company has 4,800 square feet of leather available each week. Formulate this problem as a linear programming model, and solve using the graphical method. What are the optimal number of baseballs and cricket balls that Duke Manufacturing should produce, and what is the value of profits at optimality?

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Hours Required per Ball Cutting and Dyeing Product Sewing and Packaging Profit per Unit Baseball Cricket Ball 2 1 $8 $12 2.