Question

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 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	1/8	1	$5
Catcher's model	3/2	1/4	1/2	$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. If the constant is "1" it must be entered in the box. Do not round intermediate calculation. If an amount is zero, enter "0"
	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
(b)	Develop a spreadsheet model and find the optimal solution using Solver. How many gloves of each model should Kelson manufacture? If your answer is zero enter “0”.
	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? If your answer is zero, enter “0”.
	Department Slack Time (Hours) Cutting and Sewing Finishing Packing and Shipping

Answer 1

a) The LP formulation is as shown below:

Max z=5R+7C

s.t

0.5R+1.5C<=900

0.13R+0.25C<=300

1R+0.5C<=200

R,C >=0

b)Using excel solver,the optimal solution is as shown:

Max profit=E16=SUMPRODUCT(B13:B14,B8:B9)=$ 2800

In excel,

B19=SUMPRODUCT(B13:B14,B4:B5)

B20=SUMPRODUCT(B13:B14,C4:C5)

B21=SUMPRODUCT(B13:B14,D4:D5)

The optimal solution is :

Number of gloves of Regular model=0

Number of gloves of Catcher's model=400

c)Total profit=$ 2800

d)Cutting and Sewing=600 hours

Finishing=100 hours

Packaging and shipping=200 hours

e)The slack times are as shown below:

Cutting and Sewing=300 hours

Finishing=200 hours

Packaging and shipping=0 hours