GF Incorporated, a manufacturer of power systems, uses overtime, inventory and subcontracting to absorb fluctuations in demand. An annual production plan is devised and updated quarterly. The expected demand and available capacities for the next four quarters are as follows:

Relevant cost data are as follows:
Regular production cost per unit .......$20
Overtime production cost per unit ........$25
Subcontracting cost per unit ........$30
Inventory holding cost per unit per period....$ 3
Beginning inventory ..............0
Design a production plan that will satisfy demand at minimumcost.

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Regular Overtime Subcontracting Period Demand Capacity Capacity Capacity 2000 4500 1000 7500 1000 3000 1000 1000 1000 1000 1000 5000 5000 5000 5000 1000