Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that120 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a seniordesigner and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake ViewWinery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. Toprovide 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 projectcommitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18for Sarah.(a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the projectto 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 isassigned to the project, and S is the number of hours Sarah is assigned to the project.)Min 30L + 25D + 185S.L.Minimum LisaMinimum SarahMaximum LisaMaximum SarahTaral TimeL≥0.4(D+L)$20.15(L+D+S)L≤ 50S≤ 25 (D+ L)I+D+S 120 (b) How many hours should be assigned to each graphic designer?Lisa's Hours38.4David's Hours57.6Sarah's Hours24What is the total cost (in dollars)?$ 3024✓hours✓hourshours(c) Suppose Lisa could be assigned more than 50 hours. What effect would this have on the optimal solution? Explain.The shadow price for this constraint is 50Lisa will notchange the solution.X, since the constraint is not binding ✔ Therefore, additional hours for(d) If Sarah were not required to work a minimum number of hours on this project, would the optimal solution change? Explain.The shadow price for this constraint is, since the constraint is not binding.Therefore, assigning fewer hours toSarah will notchange the solution.

For this question, I would formulate the LP problem, Then, I would use Ms. Excel solver tool and…

Answered: (b) How many hours should be assigned…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.4: Fixed-cost Models

Problem 20P

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