14. Game Day Fashions makes custom t-shirts for fans of college university sports teams. Currently, the company is trying to determine the best way to fill an order it received from Sable University. The official colors of Sable University are orange and maroon, so most of the t-shirts it orders are for one of those two colors. However, one home game each year is designated as a "white out" games where all Sable University fans are encouraged to wear white shirts. Sable University has placed an order for 50,000 orange shirts, 45,000 maroon shirts, and 30,000 white shirts. Under the terms of the contract, the company is permitted to outsource as many as 25,000 of each of the shirts from a competing company. Game Day Fashions can make the orange, maroon, and white shirts for $7.50, $3.00, and $4.00 per unit, respectively. The company handling the outsourcing has agreed to make up to 25,000 of each shirt color at a cost of $9.00, $5.00, and $4.75 per unit for the maroon, orange, and white shirts, respectively. The following table summarizes the amount of time in seconds it takes Game Day's production department to make each shirt color. Operation Orange Cutting 15 Seconds Required per Unit Maroon 10 White 12 Sewing 6 4 7 Printing 10 8 6 Game Day has 200 hours of cutting capacity available, 85 hours of sewing, and 140 hours of printing. The company would like to determine the optimal way of filling the order for Sable University. a. Formulate an LP model for this problem. b. Implement your model in a spreadsheet and solve it. c. What is the optimal solution?
14. Game Day Fashions makes custom t-shirts for fans of college university sports teams. Currently, the company is trying to determine the best way to fill an order it received from Sable University. The official colors of Sable University are orange and maroon, so most of the t-shirts it orders are for one of those two colors. However, one home game each year is designated as a "white out" games where all Sable University fans are encouraged to wear white shirts. Sable University has placed an order for 50,000 orange shirts, 45,000 maroon shirts, and 30,000 white shirts. Under the terms of the contract, the company is permitted to outsource as many as 25,000 of each of the shirts from a competing company. Game Day Fashions can make the orange, maroon, and white shirts for $7.50, $3.00, and $4.00 per unit, respectively. The company handling the outsourcing has agreed to make up to 25,000 of each shirt color at a cost of $9.00, $5.00, and $4.75 per unit for the maroon, orange, and white shirts, respectively. The following table summarizes the amount of time in seconds it takes Game Day's production department to make each shirt color. Operation Orange Cutting 15 Seconds Required per Unit Maroon 10 White 12 Sewing 6 4 7 Printing 10 8 6 Game Day has 200 hours of cutting capacity available, 85 hours of sewing, and 140 hours of printing. The company would like to determine the optimal way of filling the order for Sable University. a. Formulate an LP model for this problem. b. Implement your model in a spreadsheet and solve it. c. What is the optimal solution?
Principles of Microeconomics
7th Edition
ISBN:9781305156050
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter22: Frontiers Of Microeconomics
Section: Chapter Questions
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Transcribed Image Text:14. Game Day Fashions makes custom t-shirts for fans of college university sports teams.
Currently, the company is trying to determine the best way to fill an order it received
from Sable University. The official colors of Sable University are orange and maroon, so
most of the t-shirts it orders are for one of those two colors. However, one home game
each year is designated as a "white out" games where all Sable University fans are
encouraged to wear white shirts. Sable University has placed an order for 50,000 orange
shirts, 45,000 maroon shirts, and 30,000 white shirts. Under the terms of the contract, the
company is permitted to outsource as many as 25,000 of each of the shirts from a
competing company. Game Day Fashions can make the orange, maroon, and white shirts
for $7.50, $3.00, and $4.00 per unit, respectively. The company handling the outsourcing
has agreed to make up to 25,000 of each shirt color at a cost of $9.00, $5.00, and $4.75 per
unit for the maroon, orange, and white shirts, respectively. The following table
summarizes the amount of time in seconds it takes Game Day's production department to
make each shirt color.
Operation
Orange
Cutting
15
Seconds Required per Unit
Maroon
10
White
12
Sewing
6
4
7
Printing
10
8
6
Game Day has 200 hours of cutting capacity available, 85 hours of sewing, and 140 hours
of printing. The company would like to determine the optimal way of filling the order for
Sable University.
a. Formulate an LP model for this problem.
b. Implement your model in a spreadsheet and solve it.
c. What is the optimal solution?
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