please show work

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 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 Regular time production capacity OT prodcution capacity pe rmonth Total production capacity September October 15000 25000 November December January 14000 28000 14000 2000 Demand Shortages from previous periods (0 if none) Beginning Inventory Production RT Production OT Shipments Shortage T Ending Inventory 4000 Required minimum ending inventory. s Shortage cost Inventory holding cost Overtime cost TOTAL COST OT prodcution capacity permonth Total production capacity 5 September October 15000 25000 November December January 14000 28000 14000 0 2000 8 Demand Shortages from previous 9 periods (o if none) 10 Beginning Inventory 11 Production RT 12 Production OTS 13 Shipments 14 Shortage Ending Inventory 4000 Required minimum ending inventory. 16 Shortage cost 17 Inventory holding cost 18 Overtime cost 19 TOTAL COST Total cost for all 5 20 periods