Industrial Designs has been awarded a contract to design a label for a new wine produced by Princess M Wineries. The company estimates that 150 hours will be required to complete the project. The firm will use three designers on the project: Lisa is a senior designer and team leader, David a senior designer, and Sarah, a junior designer. Lisa is the most experienced designer and she must be assigned at least 40% of the hours assigned to the two senior designers. Sarah needs experience and she must be assigned at least 15% of the project's hours. But, Sarah must be assigned less than 25% of the total hours assigned to the two senior designers. Due to other project committments, Lisa has a maximum of 50 hours available to work on this project. Hourly rates are $30 for Lisa, $25 for David, $18 for Sarah.
a. Write a linear program model that can be used to determine the number of hours each designer should be assigned to the project to minimize costs.
b. How many hours should each designer be assigned? What is the total cost?