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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 to maximize profit. a. Formulate an integer programming model for this problem. b. Solve this model by using the computer. Compare this solution with the solution with- out integer restrictions, and indicate whether the rounded-down solution would have been optimal.

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 to maximize profit. a. Formulate an integer programming model for this problem. b. Solve this model by using the computer. Compare this solution with the solution with- out integer restrictions, and indicate whether the rounded-down solution would have been optimal.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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1. Formulate a linear or integer model (clearly statedecision variables, objective, and constraints) 2. Find the optimal solution using Excel Solver 3. Do not solve graphically 4. Answer all questions 5. Attach your solver files and formulations.
Transcribed Image Text:1. Formulate a linear or integer model (clearly statedecision variables, objective, and constraints) 2. Find the optimal solution using Excel Solver 3. Do not solve graphically 4. Answer all questions 5. Attach your solver files and formulations.
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 to maximize profit. a. Formulate an integer programming model for this problem. b. Solve this model by using the computer. Compare this solution with the solution with- out integer restrictions, and indicate whether the rounded-down solution would have been optimal.
Transcribed Image Text: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 to maximize profit. a. Formulate an integer programming model for this problem. b. Solve this model by using the computer. Compare this solution with the solution with- out integer restrictions, and indicate whether the rounded-down solution would have been optimal.
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