Western Sports Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table.
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Production Time (hours)
Cutting Packaging
Model and Sewing Finishing and Shipping Profit/Glove
Regular model 1 ½ 1/8 $5
Catcher's model 3/2 1/3 ¼ $8
Assuming that the company is interesting in maximizing the total profit contribution, answer the following:
a. What is the linear programming model for this problem?
b. Find the optimal solution using the graphical solution procedure. How many gloves of each model should Western Sports manufacture?
c. What is the total profit contribution Western Sports can earn with the listed production quantities?