# Math

22. Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 150 hours will be required to complete the project. The firm’s three graphics 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, Sarah 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 in order to minimize total cast.
b. How many hours should each graphic designer be assigned to the project? What is the total cost?
c. Suppose Lisa could be assigned more than 50 hours. What effect would this have on the optimal solution? Explain.
d. If Sarah were not required to work a minimum number of hours on this project, would the optimal solution change? Explain.

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