1. (10 POINTS) Suppose that demand data for widgets made by XYZ Inc. is given below. Using an appropriate method (level , chase or mixed), plan the production (i.e. specify the production quantities and complete the table below) such that the total cost is made as small as possible. Regular time production capacity is 9000 units per month. Over time production capacity is 2000 units per month. Overtime costs $3.00 per unit extra. There is no other method of production and the cost of regular time work force is fixed and it does not depend on the amount produced and hence may be omitted in the cost calculations. Holding cost per unit per month is $6.00 (special facilities are needed to store and hence the high cost), and shortage cost is $1.00 per unit per month, (short units must be supplied at a later period, but within the 5 month planning horizon.) what is the total inventory holding cost (use ending inventory to calculate this cost), total shortage cost and the total cost of your plan? Try to find the best plan with the lowest total cost.

	September	October	November	December	January
Demand	14000	10000	5000	11000	3000
Shortages from previous periods (0 if none)	0
Beginning Inventory	2000
Production RT
Production OT
Shipments
Shortage
Ending Inventory					Should be at least 2000
Shortage cost
Inventory holding cost
Overtime cost
TOTAL COST

Total Production needed during the 5 months = ______________;

Total capacity (RT and OT) Available during the 5 months = _______________

Total cost of the Plan: