We discussed the three main components of a linear programming problem namely objective function, constraints, and the non-negativity constraints. Discuss how you can formulate this problem as an LP problem starting with the definition of the decision variables. Identify the constraints, etc. After the discussion session,solve the problem using the graphical method.
Kelson Sporting 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 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
3/2
1/3
1/4
$8
Assuming the company is interested in maximizing the total profit contribution, answer the following:
What is the linear programming model for this problem?
Find the optimal solution using the graphical solution procedure. How many gloves of each model should Kelson manufacture?
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?
What is the slack time in each department?
Sample Solution