Question: The Paris Paint Company is in the process of planning labor force requirements and production levels for the next four quarters. The marketing department has provided production with the following forecasts of demand for Paris Paint over the next year:

                                       Demand Forecast

Quarter                           (in thousands of gallons)

1                                            380

2                                            630

3                                            220

4                                            160

Assume that there are currently 280 employees with the company. Employees are hired for at least one full quarter. Hiring costs amount to $1,200 per employee and firing costs are $2,500 per employee. Inventory costs are $1 per gallon per quarter. It is estimated that one worker produces 1,000 gallons of paint each quarter. Assume that Paris currently has 80,000 gallons of paint in inventory and would like to end the year with an inventory of at least 20,000 gallons.

a. Determine the minimum constant workforce plan for Paris Paint and the cost of the plan. Assume that stock-outs are not allowed.

b. If Paris were able to back-order excess demand at a cost of $2 per gallon per quarter, determine a minimum constant workforce plan that holds less inventory than the plan you found in part (a), but incurs stock-outs in quarter 2. Determine the cost of the new plan.

c. Formulate this as a linear program. Assume that stock-outs are not allowed.

d. Solve the linear program. Round the variables and determine the cost of the resulting plan.