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Prob 1. (80 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 during regular time and overtime for each month, and complete the table below) such that the total cost is made as small as possible. Regular time production capacity is 20000 units per month. Over time production capacity is 5000 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 $2.00, and shortage cost is $9.00 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. Total production needed for the 5 months Regular time production capacity per month OT prodcution capacity pe rmonth Total production capacity September 15000 October 25000 November 14000 December 28000 January 14000 Demand 0 2000 Shortages from previous periods (o if none) Beginning Inventory Production RT Production OT Shipments Shortage Ending Inventory 4000