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 $$7\mathrm{.}50,$ the cost of subcontracting is $$9$ per

unit, and the cost of carrying a unit in inventory from one month to the next is $$2.$

Month Jan Feb Mar Apr May

Forecast $5007501200650300$

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 stockouts.