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A food wholesaler has three kinds of individual bags of potato chips: regular, barbeque, and salt and vinegar. She wants to sell the bags of chips in bulk packages. The bronze package consists of 20 bags of regular and 10 bags of barbeque. The silver package contains 20 bags of regular, 10 bags of barbeque, and 10 bags of salt and vinegar. The gold package consists of 30 bags of regular, 10 bags of barbeque, and 10 bags of salt and vinegar. The profit is $10 on each bronze package, $30 on each silver package, and $40 on each gold package. The food wholesaler has a total of 8500 bags of regular chips, 3100 bags of barbeque, and 2400 bags of salt and vinegar. Assume all the packages will be sold. Use the simplex method to complete parts (a) and (b). ..... (a) How many gold, silver, and bronze packages should be made up in order to maximize profit? What is the maximum profit? Set up the linear programming problem. Let x1, x2, and x3 represent the numbers of bronze, silver, and gold packages made up, respectively, and let z be the total profit. Maximize z= 10x, + 30x2 + 40x3 subject to 20x, +20x2 + 30x3 s 8500 10x1 + 10x2 + 10x3 s 3100 10x2 + 10x3 s 2400 X1 20, x2 2 0, x320. (Do not factor. Do not include the $ symbol in your answers.) The maximum profit is $ 10250 . To get that profit, 65 bronze packages, 0 silver packages, and 240 gold packages should be made up. (Type whole numbers.) (b) Explain what the values of the slack variables in the optimal solution mean in the context of the problem. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. When the profit is maximized, all of the bags of barbeque chips and salt and vinegar chips are used, but (Type a whole number.) bags of regular chips are unused. O B. When the profit is maximized, all of the bags of each kind of chips are used. O C. When the profit is maximized, all of the bags of regular chips and salt and vinegar chips are used, but bags of barbeque chips are unused. (Type a whole number.) O D. When the profit is maximized, all of the bags of regular chips and barbeque chips are used, but bags of salt and vinegar chips are unused. (Type a whole number.) O E. When the profit is maximized, all of the bags of barbeque chips are used, but (Type whole numbers.) bags of regular chips and bags of salt and vinegar chips are unused.

A food wholesaler has three kinds of individual bags of potato chips: regular, barbeque, and salt and vinegar. She wants to sell the bags of chips in bulk packages. The bronze package consists of 20 bags of regular and 10 bags of barbeque. The silver package contains 20 bags of regular, 10 bags of barbeque, and 10 bags of salt and vinegar. The gold package consists of 30 bags of regular, 10 bags of barbeque, and 10 bags of salt and vinegar. The profit is $10 on each bronze package, $30 on each silver package, and $40 on each gold package. The food wholesaler has a total of 8500 bags of regular chips, 3100 bags of barbeque, and 2400 bags of salt and vinegar. Assume all the packages will be sold. Use the simplex method to complete parts (a) and (b). ..... (a) How many gold, silver, and bronze packages should be made up in order to maximize profit? What is the maximum profit? Set up the linear programming problem. Let x1, x2, and x3 represent the numbers of bronze, silver, and gold packages made up, respectively, and let z be the total profit. Maximize z= 10x, + 30x2 + 40x3 subject to 20x, +20x2 + 30x3 s 8500 10x1 + 10x2 + 10x3 s 3100 10x2 + 10x3 s 2400 X1 20, x2 2 0, x320. (Do not factor. Do not include the $ symbol in your answers.) The maximum profit is $ 10250 . To get that profit, 65 bronze packages, 0 silver packages, and 240 gold packages should be made up. (Type whole numbers.) (b) Explain what the values of the slack variables in the optimal solution mean in the context of the problem. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. When the profit is maximized, all of the bags of barbeque chips and salt and vinegar chips are used, but (Type a whole number.) bags of regular chips are unused. O B. When the profit is maximized, all of the bags of each kind of chips are used. O C. When the profit is maximized, all of the bags of regular chips and salt and vinegar chips are used, but bags of barbeque chips are unused. (Type a whole number.) O D. When the profit is maximized, all of the bags of regular chips and barbeque chips are used, but bags of salt and vinegar chips are unused. (Type a whole number.) O E. When the profit is maximized, all of the bags of barbeque chips are used, but (Type whole numbers.) bags of regular chips and bags of salt and vinegar chips are unused.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 61P
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A food wholesaler has three kinds of individual bags of potato chips: regular, barbeque, and salt and vinegar. She wants to sell the bags of chips in bulk packages. The bronze package consists of 20 bags of regular and 10 bags of barbeque. The silver package contains 20 bags of regular, 10 bags of barbeque, and 10 bags of salt and vinegar. The gold package consists of 30 bags of regular, 10 bags of barbeque, and 10 bags of salt and vinegar. The profit is $10 on each bronze package, $30 on each silver package, and $40 on each gold package. The food wholesaler has a total of 8500 bags of regular chips, 3100 bags of barbeque, and 2400 bags of salt and vinegar. Assume all the packages will be sold. Use the simplex method to complete parts (a) and (b). ..... (a) How many gold, silver, and bronze packages should be made up in order to maximize profit? What is the maximum profit? Set up the linear programming problem. Let x,, X2, and x3 represent the numbers of bronze, silver, and gold packages made up, respectively, and let z be the total profit. Maximize z= 10x1 +30x2 + 40x3 subject to 20х1 + 20х2 + 30хз 5 8500 10x1 + 10х2 + 10х3 S 3100 10х2 + 10xз S 2400 X1 20, x2 20, x3 20. (Do not factor. Do not include the $ symbol in your answers.) The maximum profit is $ 10250 . To get that profit, 65 bronze packages, 0 silver packages, and 240 gold packages should be made up. (Type whole numbers.) (b) Explain what the values of the slack variables in the optimal solution mean in the context of the problem. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. When the profit is maximized, all of the bags of barbeque chips and salt and vinegar chips are used, but bags of regular chips are unused. (Type a whole number.) B. When the profit is maximized, all of the bags of each kind of chips are used. C. When the profit is maximized, all of the bags of regular chips and salt and vinegar chips are used, but (Type a whole number.) bags of barbeque chips are unused. D. When the profit is maximized, all of the bags of regular chips and barbeque chips are used, but bags of salt and vinegar chips are unused. (Type a whole number.) E. When the profit is maximized, all of the bags of barbeque chips are used, but bags of regular chips and bags of salt and vinegar chips are unused. (Type whole numbers.)
Transcribed Image Text:A food wholesaler has three kinds of individual bags of potato chips: regular, barbeque, and salt and vinegar. She wants to sell the bags of chips in bulk packages. The bronze package consists of 20 bags of regular and 10 bags of barbeque. The silver package contains 20 bags of regular, 10 bags of barbeque, and 10 bags of salt and vinegar. The gold package consists of 30 bags of regular, 10 bags of barbeque, and 10 bags of salt and vinegar. The profit is $10 on each bronze package, $30 on each silver package, and $40 on each gold package. The food wholesaler has a total of 8500 bags of regular chips, 3100 bags of barbeque, and 2400 bags of salt and vinegar. Assume all the packages will be sold. Use the simplex method to complete parts (a) and (b). ..... (a) How many gold, silver, and bronze packages should be made up in order to maximize profit? What is the maximum profit? Set up the linear programming problem. Let x,, X2, and x3 represent the numbers of bronze, silver, and gold packages made up, respectively, and let z be the total profit. Maximize z= 10x1 +30x2 + 40x3 subject to 20х1 + 20х2 + 30хз 5 8500 10x1 + 10х2 + 10х3 S 3100 10х2 + 10xз S 2400 X1 20, x2 20, x3 20. (Do not factor. Do not include the $ symbol in your answers.) The maximum profit is $ 10250 . To get that profit, 65 bronze packages, 0 silver packages, and 240 gold packages should be made up. (Type whole numbers.) (b) Explain what the values of the slack variables in the optimal solution mean in the context of the problem. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. When the profit is maximized, all of the bags of barbeque chips and salt and vinegar chips are used, but bags of regular chips are unused. (Type a whole number.) B. When the profit is maximized, all of the bags of each kind of chips are used. C. When the profit is maximized, all of the bags of regular chips and salt and vinegar chips are used, but (Type a whole number.) bags of barbeque chips are unused. D. When the profit is maximized, all of the bags of regular chips and barbeque chips are used, but bags of salt and vinegar chips are unused. (Type a whole number.) E. When the profit is maximized, all of the bags of barbeque chips are used, but bags of regular chips and bags of salt and vinegar chips are unused. (Type whole numbers.)
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