Question: The staff demand at UNC student store in terms of hours per week is given below:

At the beginning of each week, the store hires students to fulfill its staff demand. Students hired in weeks 1 or 3 work for 2 consecutive weeks (i.e., a student hired in week 1 works for weeks 1 and 2); each of these students works for 15 hours per week and is paid $400 in total. Students hired in week 2 work for 3 consecutive weeks; each of them works for 10 hours per week and is paid $270 in total. Students hired in week 4 work only for 1 week; each of them works for 5 hours per week and is paid $65 in total. In each week, the student store needs to have total student working hours no less than its weekly demand described in the table above.

a. Formulate a linear programming model to determine UNC student store’s optimal hiring plan (i.e., the number of students hired at the beginning of each week) to minimize its total cost. [13%]

b. Solve the model using Excel Solver. [5%]