(solution) Kelson Sporting Equipment, Inc., makes two different types of

(solution) Kelson Sporting Equipment, Inc., makes two different types of

Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher’s model. The firm has 600 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 200 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 1/2 1 1/6 $4
Catcher’s model 3/2 1/2 1/2 $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? 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.
 
Max  R +  C
s.t.
 R +  C – Select your answer -??=Item 5    Cutting and sewing
 R +  C – Select your answer -??=Item 9    Finishing
 R +  C – Select your answer -??=Item 13    Packing and Shipping
R, C – Select your answer -??=Item 15  0
   
(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?
   
(d) 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