Gang Aft Agley, a manufacturing company, faces the aggregate planning problem shown in the table below. Cost of regular production is $5 per unit, the cost of producing the same unit on overtime is $7.50, the cost of subcontracting is $9 per unit, and the cost of carrying a unit in inventory from one month to the next is $2.

	January	February	March	April	May
Forecast	500	750	1200	650	300
Beginning Inventory	100
Regular Time
Overtime
Subcontracting
Ending Inventory

The labor contract at the plant prohibits both overtime and subcontracting output to exceed 300 units in any five month window. The plant capacity is 600 units per month produced using two shifts, regardless of the number of days in a month. By policy, management wants to avoid stock outs.

Formulate the aggregate plan using linear programming.