Reference no: EM132901851

1. The staff demand at the Johns Hopkins student store in terms of hours per week is given below:

Week Staff Demand (hours)

1 300

2 340

3 345

4 265

At the beginning of each week, the store hires students to fulfill its staff demand. Students hired in week 1 work for 3 consecutive weeks (i.e., a student hired in week 1 works for weeks 1, 2, and 3); each of these students works for 15 hours per week and is paid $450 in total. Students hired in weeks 2 and 4 work only for 1 week; each of them works for 20 hours per week and is paid $180 in total. Students hired in week 3 work for 2 weeks; each of them works for 15 hours per week and is paid $290 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 Johns Hopkins student store's optimal hiring plan (i.e., the number of students hired at the beginning of each week) to minimize its total cost.

b. Solve the model using Excel Solver. Please do not use integer constraints

c. In this year, week 4 coincides with a national holiday; as a result there is more staff demand in week 4. Suppose week 4's staff demand for this year is 305 hours instead of the normal 265 hours. Without re-solving your optimization model, please answer the following questions:

i) Does the total cost change? If so, by how much?

ii) Do you now hire a different number of students in the optimal solution? How do you know? Please note that simply answering a number or "yes" or "no" without justification/calculation does not give you any credit.

d. Let's consider a new scenario: suppose that week 4 coincides with a national holiday. The staff demand does not change, but we decide to increase student's wage in week 4 from $180 to $240. Without re-solving your optimization model, please answer the following questions using the sensitivity report:

iii) Does the optimal solution change?

iv) What is the new cost?