Problem 11-1

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 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	3/2	1/3	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? Enter the answers as fractions or round the answers to 3 decimal places.

LetR	= 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