Question: Kelson Sporting Equipment, Inc., makes two 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:
Production Time (hours)
Model Cutting and Sewing Finishing Packaging and Shipping Profit/Glove
Regular model 1 1/2 1/8 $5
Catcher's model 1/2 1/8 1/4 $8
Assuming that the company is interested in maximizing the total profit contribution, answer the following:
a. What is the linear programming model for this problem?
b. Develop a spreadsheet model and find the optimal solution using Excel Solver. How many of each model should Kelson manufacture?
c. What is the total profit contribution Kelson can earn with the optimal production quantities?
d. How many hours of production time will be scheduled in each department?
e. What is the slack time in each department?