Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model.
The firm has 800 hours of production time available in its cutting and sewing department, 150 hours available in its finishing department, and 400 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 |
1/4 |
1/6 |
$5 |
| Catcher's model |
1/2 |
1/2 |
1/4 |
$7 |
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? If required, round your answers to 3 decimal places or enter your answers as a fraction.
Let R = number of units of regular model.
C = number of units of catcher's model.
B. Develop a spreadsheet model and find the optimal solution using Solver. How many gloves of each model should Kelson manufacture?
Regular Model = units
Catcher's Model = units
(c) What is the total profit contribution Kelson can earn with the given production quantities?
How many hours of production time will be scheduled in each department?
Department Time Used (Hours)
Cutting and sewing
Finishing
Packing and Shipping
(e) What is the slack time in each department?
Department Slack Time (Hours)
Cutting and sewing
Finishing
Packing and Shipping