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a. Create a set of linear equations to describe the objective function and the constraints. b. Use graphic analysis to find the visual solution. c. What combination of business and nonbusiness courses minimizes total hours of study?

a. Create a set of linear equations to describe the objective function and the constraints. b. Use graphic analysis to find the visual solution. c. What combination of business and nonbusiness courses minimizes total hours of study?

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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BUSS211 Operations Management HW#4 Due 6/3 (Fri) 11:59 pm #1. A business student at Nowledge College must complete a total of 65 courses to graduate. The number of business courses must be greater than or equal to 23. The number of nonbusiness courses must be greater than or equal to 20. The average business course requires a textbook costing $60 and 120 hours of study. Nonbusiness courses require a textbook costing $24 and 200 hours of study. The student has $3,000 to spend on books. a. Create a set of linear equations to describe the objective function and the constraints. b. Use graphic analysis to find the visual solution. c. What combination of business and nonbusiness courses minimizes total hours of study? d. Identify the slack or surplus variables. #2. In Problem 1, suppose that the objective is to minimize the cost of books and that the student's total study time is limited to 12,600 hours. a. Use graphic analysis to determine the combination of courses that minimizes the total cost of books. b. Identify the slack or surplus variables.
Transcribed Image Text:BUSS211 Operations Management HW#4 Due 6/3 (Fri) 11:59 pm #1. A business student at Nowledge College must complete a total of 65 courses to graduate. The number of business courses must be greater than or equal to 23. The number of nonbusiness courses must be greater than or equal to 20. The average business course requires a textbook costing $60 and 120 hours of study. Nonbusiness courses require a textbook costing $24 and 200 hours of study. The student has $3,000 to spend on books. a. Create a set of linear equations to describe the objective function and the constraints. b. Use graphic analysis to find the visual solution. c. What combination of business and nonbusiness courses minimizes total hours of study? d. Identify the slack or surplus variables. #2. In Problem 1, suppose that the objective is to minimize the cost of books and that the student's total study time is limited to 12,600 hours. a. Use graphic analysis to determine the combination of courses that minimizes the total cost of books. b. Identify the slack or surplus variables.
#3. The Sports Shoe Company is a manufacturer of basketball and football shoes. The manager of marketing must decide the best way to spend advertising resources. Each football team sponsored requires 120 pairs of shoes. Each basketball team requires 32 pairs of shoes. Football coaches receive $300,000 for shoe sponsorship, and basketball coaches receive $1,000,000. The manager's promotional budget is $30,000,000. The company has a limited supply (4 liters, or 4,000 cubic centimeters) of flubber, a rare and costly compound used in promotional athletic shoes. Each pair of basketball shoes requires 3 cc of flubber, and each pair of football shoes requires 1 cc. The manager wants to sponsor as many basketball and football teams as resources will allow. a. Create a set of linear equations to describe the objective function and the constraints. b. Use graphic analysis to find the visual solution. c. What is the maximum number of each type of team that the company can sponsor? #4. Mile-High Microbrewery makes a light beer and a dark beer. Mile-High has a limited supply of barley, limited bottling capacity, and a limited market for light beer. Profits are $0.20 per bottle of light beer and $0.50 per bottle of dark beer. a. The following table shows resource availability of products at the Mile- High Microbrewery. Use the graphic method of linear programming to maximize profits. How many bottles of each product should be produced per month? PRODUCT Light Beer Dark Beer Resource Resource Availability (per month) (x₁) (x₂) Barley 0.1 gram 0.6 gram 2,000 grams Bottling 1 bottle 1 bottle 6,000 bottles Market 1 bottle 4,000 bottles b. Identify any constraints with slack or surplus.
Transcribed Image Text:#3. The Sports Shoe Company is a manufacturer of basketball and football shoes. The manager of marketing must decide the best way to spend advertising resources. Each football team sponsored requires 120 pairs of shoes. Each basketball team requires 32 pairs of shoes. Football coaches receive $300,000 for shoe sponsorship, and basketball coaches receive $1,000,000. The manager's promotional budget is $30,000,000. The company has a limited supply (4 liters, or 4,000 cubic centimeters) of flubber, a rare and costly compound used in promotional athletic shoes. Each pair of basketball shoes requires 3 cc of flubber, and each pair of football shoes requires 1 cc. The manager wants to sponsor as many basketball and football teams as resources will allow. a. Create a set of linear equations to describe the objective function and the constraints. b. Use graphic analysis to find the visual solution. c. What is the maximum number of each type of team that the company can sponsor? #4. Mile-High Microbrewery makes a light beer and a dark beer. Mile-High has a limited supply of barley, limited bottling capacity, and a limited market for light beer. Profits are $0.20 per bottle of light beer and $0.50 per bottle of dark beer. a. The following table shows resource availability of products at the Mile- High Microbrewery. Use the graphic method of linear programming to maximize profits. How many bottles of each product should be produced per month? PRODUCT Light Beer Dark Beer Resource Resource Availability (per month) (x₁) (x₂) Barley 0.1 gram 0.6 gram 2,000 grams Bottling 1 bottle 1 bottle 6,000 bottles Market 1 bottle 4,000 bottles b. Identify any constraints with slack or surplus.
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