3. Consider the aggregate planning context provided on Appendix 2.

a) What is the minimum constant workforce that would allow you to comply with all the demand, the safety stock rule for every month and the minimum allowed inventory at the end of the period? (15 points)

b) Formulate this aggregate planning problem as a Linear Program (10 points)

c) Solve the Linear program and provide optimal solution for the cost function and all variables (15 points).

Appendix 2: Aggregate planning context for Problem 3

Aggregate demand forecast

Month	Demand Forecast
January	870
February	460
March	800
April	1300
May	2100

Current workforce and Inventory

Initial Workforce: 250 workers

Initial Inventory: 400 aggregate units

Costs

Hiring Cost = $400/worker

Layoff Cost = $1200/worker

Salary = $1000/worker-month

Inventory cost = $10/unit-month

Business rules

Minimum allowed inventory at end of planning period: 450 units

Safety stock (minimum allowed inventory on any month): 100 units

Further information

It was observed that in two months with a workforce of 120 workers, the production was 500 aggregate units