1. The staff demand at a college Student Stores for the 4 busiest consecutive weeks of a year is given below:

Week	Staff Demand (hours)
1	330
2	450
3	390
4	410

The store hires students to fulfill its staff demand in these weeks. Students hired at the beginning of weeks 1 or 3 work for 2 consecutive weeks (e.g., a student hired in week 1 works for weeks 1 and 2); in each week, each student works for 15 hours and is paid $200. Students hired at the beginning of week 2 work for 3 consecutive weeks; in each week, each student works for 10 hours and is paid $100. Students hired at the beginning of week 4 work only for 1 week; each student works for 5 hours and is paid $65. In each week, Student Stores needs to have total student working hours no less than its weekly demand described in the table above.

1. Formulate a linear programming model to determine Student Stores optimal hiring plan (i.e., the number of students hired at the beginning of each week) to minimize its total cost.
2. Solve the model using Excel Solver.
3. Students hired in weeks 1 and 3 work for 15 hours per week in 2 consecutive weeks, and are paid $200 per week. Does this lead your optimal solution to hire the same number of students in weeks 1 and 3? If not, in which week do you hire more students? Do you have an intuitive explanation why this is the case?
4. In this year, week 4 coincides with a national holiday; as a result there is more staff demand in week 4. Suppose week 4s staff demand for this year is 430 hours instead of the normal 410 hours. Without re-solving your optimization model, please answer the following questions (need reasoning

1. Does the total cost change? If so, by how much?
2. Do you now hire a different number of students in the optimal solution? How do you know?