Industrial design has been awarded a contract todesign a label for a new wine produced by Lake View Winery.Thecompany estimates that150 hours will be required to complete theproject.The firm's three graphic designers available for to thisproject are Lisa,a senior designer and team leader; David , asenior designer; and Sarah, a junior designer. Because Lisa hasworked on several projects for Lake View Winery, management hasspecified that Lisa must be assigned at least 40%of the totalnumber of hours assigned to the two senior designers. To providelabel -designing experience for Sarah, she must be assigned atleast 15% of the total project time. However, the number of hoursassigned to Sarah. must not exceed 25% of the total number of hoursassigned to the two senior designers.   Due to othercommitments, Lisa has a maximum of 50 hours available to work onthis project. Hourly wage rates are $30 for Lisa, $25 for David,and $18 for Sarah.

a. Formulate a linear program that can be used todetermine the number of hours each graphic designer should beassigned to the project in order to minimize the total cost.

b. How many hours should each graphic designer beassigned to the project?

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 numberof hours on this project, would the optimal solution change?Explain.