The forecasted demand in aggregate units for April is given as 4XXX. You need to replace XXX with the last 3 digits of your Student ID number. For example, if your student ID number is 105987, you will use a forecasted value of 4987 microwave ovens for April.

A normal work-day is eight hours. Hiring costs are OMR 650 per worker and firing costs are OMR 1950 per worker. Holding costs are OMR 5 per aggregate unit held per month, and backorder cost is OMR 45 per aggregate unit per month. It requires an average of 50 minutes for one worker to assemble one oven. The ending inventory in December of the previous year was 225 units, and the manager wants to have at least 120 units on hand in inventory at the end of June. The workforce at the end of December in the previous year was 20 workers. Workers are paid OMR 6 per hour for regular time labor. Overtime labor costs OMR 9 per worker per hour, and the maximum overtime that is allowed is 3 hours per worker each day.

(a) Find the minimum constant workforce plan for the six months and the total cost of the plan. The firm does not want any stockouts. The plan should show the production levels, workforce levels, number hired, number fired, ending inventory and shortages for each month. You may hire or fire workers only at the beginning of January. What is the cost of this plan?

(b) Determine the zero inventory (chase) plan that hires and fires workers each month to match demand as closely as possible, and the cost of that plan. No stockouts are allowed.

(c) Prepare an Excel sheet to generate the aggregate production plan for part (b). Use this Excel sheet to find the total cost if the forecast demand for February is changed to 3500 microwave ovens.

(d) Formulate the problem as a linear programming model to find the best aggregate production plan.

(e) Use Excel Solver to find a feasible aggregate production plan through the conservative approach. Explain.

Month	Workdays	Forecasted demand
Jan	22	3325
Feb	18	3940
Mar	23	4825
Apr	20	4987
May	23	4780
June	19	4425