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A tailor makes wool tweed sport coats and wool slacks. He is able to get a shipment of 150 square yards of wool cloth from Scotland each month to make coats and slacks, and he has 200 hours of his own labor to make them each month. A coat requires 3 square yards of wool and 10 hours to make, and a pair of pants requires 5 square yards of wool and 4 hours to make. He earns $50 in profit from each coat he makes and $40 from each pair of slacks. He wants to know how many coats and slacks to produce to maximize profit. a. Formulate an integer linear programming model for this problem. b. Determine the integer solution to this problem using the branch and bound method. Compare this solution with the solution without integer restrictions and indicate if the rounded-down solution would have been optimal.

A tailor makes wool tweed sport coats and wool slacks. He is able to get a shipment of 150 square yards of wool cloth from Scotland each month to make coats and slacks, and he has 200 hours of his own labor to make them each month. A coat requires 3 square yards of wool and 10 hours to make, and a pair of pants requires 5 square yards of wool and 4 hours to make. He earns $50 in profit from each coat he makes and $40 from each pair of slacks. He wants to know how many coats and slacks to produce to maximize profit. a. Formulate an integer linear programming model for this problem. b. Determine the integer solution to this problem using the branch and bound method. Compare this solution with the solution without integer restrictions and indicate if the rounded-down solution would have been optimal.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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 Formulate and solve the following 2 problems, using Branch and bound method

+ X Assignment 1.DS.pdf X Assignment 1.DS.pdf X Bernard W Taylor - Chapter 1 Ma PDE PDF C:/Users/Nourhan/Downloads/Video/Assignment%201.DS.pdf )( ملف V A | D 6 js Q5: Formulate and solve the following 2_problems, using Branch and bound method A tailor makes wool tweed sport coats and wool slacks. He is able to get a shipment of 150 square yards of wool cloth from Scotland each month to make coats and slacks, and he has 200 hours of his own labor to make them each month. A coat requires 3 square yards of wool and 10 hours to make, and a pair of pants requires 5 square yards of wool and 4 hours to make. He earns $50 in profit from each coat he makes and $40 from each pair of slacks. He wants to know how many coats and slacks to produce to maximize profit. a. Formulate an integer linear programming model for this problem. b. Determine the integer solution to this problem using the branch and bound method. Compare this solution with the solution without integer restrictions and indicate if the rounded-down solution would have been optimal.
Transcribed Image Text:+ X Assignment 1.DS.pdf X Assignment 1.DS.pdf X Bernard W Taylor - Chapter 1 Ma PDE PDF C:/Users/Nourhan/Downloads/Video/Assignment%201.DS.pdf )( ملف V A | D 6 js Q5: Formulate and solve the following 2_problems, using Branch and bound method A tailor makes wool tweed sport coats and wool slacks. He is able to get a shipment of 150 square yards of wool cloth from Scotland each month to make coats and slacks, and he has 200 hours of his own labor to make them each month. A coat requires 3 square yards of wool and 10 hours to make, and a pair of pants requires 5 square yards of wool and 4 hours to make. He earns $50 in profit from each coat he makes and $40 from each pair of slacks. He wants to know how many coats and slacks to produce to maximize profit. a. Formulate an integer linear programming model for this problem. b. Determine the integer solution to this problem using the branch and bound method. Compare this solution with the solution without integer restrictions and indicate if the rounded-down solution would have been optimal.
+ X Assignment 1.DS.pdf X Assignment 1.DS.pdf X Bernard W Taylor - Chapter 1 Ma PDE PDF C:/Users/Nourhan/Downloads/Video/Assignment%201.DS.pdf ( ملف V A D 6 js A jeweler and her apprentice make silver pins and necklaces by hand. Each week they have 80 hours of labor and 36 ounces of silver available. It requires 8 hours of labor and 2 ounces of silver to make a pin, and 10 hours of labor and 6 ounces of silver to make a necklace. Each pin also contains a small gem of some kind. The demand for pins is no more than six per week. A pin earns the jeweler $400 in profit, and a necklace earns $100. The jeweler wants to know how many of each item to make each week in order to maximize profit. a. Formulate an integer programming model for this problem. b. Solve this model using the branch and bound method. Compare this solution with the solu- tion without integer restrictions and indicate if the rounded-down solution would have been optimal.
Transcribed Image Text:+ X Assignment 1.DS.pdf X Assignment 1.DS.pdf X Bernard W Taylor - Chapter 1 Ma PDE PDF C:/Users/Nourhan/Downloads/Video/Assignment%201.DS.pdf ( ملف V A D 6 js A jeweler and her apprentice make silver pins and necklaces by hand. Each week they have 80 hours of labor and 36 ounces of silver available. It requires 8 hours of labor and 2 ounces of silver to make a pin, and 10 hours of labor and 6 ounces of silver to make a necklace. Each pin also contains a small gem of some kind. The demand for pins is no more than six per week. A pin earns the jeweler $400 in profit, and a necklace earns $100. The jeweler wants to know how many of each item to make each week in order to maximize profit. a. Formulate an integer programming model for this problem. b. Solve this model using the branch and bound method. Compare this solution with the solu- tion without integer restrictions and indicate if the rounded-down solution would have been optimal.
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