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Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 120 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah. (a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.) Min 30L +25D+18S s.t. Minimum Lisa Minimum Sarah L≥0.4(L+D) S≥0.15(D+L+S) Maximum Lisa L≤ 50 Maximum Sarah Total Time L, D, S≥ 0 S≤0.25(L+D) L+D+S 120 (b) How many hours should be assigned to each graphic designer? Lisa's Hours David's Hours Sarah's Hours What is the total cost (in dollars)? $ × hours × hours × hours

Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 120 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah. (a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.) Min 30L +25D+18S s.t. Minimum Lisa Minimum Sarah L≥0.4(L+D) S≥0.15(D+L+S) Maximum Lisa L≤ 50 Maximum Sarah Total Time L, D, S≥ 0 S≤0.25(L+D) L+D+S 120 (b) How many hours should be assigned to each graphic designer? Lisa's Hours David's Hours Sarah's Hours What is the total cost (in dollars)? $ × hours × hours × hours

Managerial Economics: A Problem Solving Approach
Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter4: Extent (how Much) Decisions
Section: Chapter Questions
Problem 3MC
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Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 120 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah. (a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.) Min 30L +25D+18S s.t. Minimum Lisa Minimum Sarah L≥0.4(L+D) S≥0.15(D+L+S) Maximum Lisa L≤ 50 Maximum Sarah Total Time L, D, S≥ 0 S≤0.25(L+D) L+D+S 120 (b) How many hours should be assigned to each graphic designer? Lisa's Hours David's Hours Sarah's Hours What is the total cost (in dollars)? $ × hours × hours × hours
Transcribed Image Text:Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 120 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah. (a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.) Min 30L +25D+18S s.t. Minimum Lisa Minimum Sarah L≥0.4(L+D) S≥0.15(D+L+S) Maximum Lisa L≤ 50 Maximum Sarah Total Time L, D, S≥ 0 S≤0.25(L+D) L+D+S 120 (b) How many hours should be assigned to each graphic designer? Lisa's Hours David's Hours Sarah's Hours What is the total cost (in dollars)? $ × hours × hours × hours
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