POS Food would like to develop an aggregate plan for producing food ingredient. The following is the related information.

Sales Period July August September Estimated Demand 1000 1200 800 Capacity(regular) 900 1000 800 Capacity(Overtime) 100 200 50

Regular production cost is $20/unit and overtime production cost is $30/unit. The initial inventory is 500 units. Inventory holding cost is $1/unit/month. Because of the expiration issue, the produced units can serve the demand at current or the next month. Thus, the initial inventory can satisfy the demand at July only and the production at July can satisfy the demand at July and August. The total cost will be calculated by the sum of the production cost plus the inventory holding cost. According to the companys policy, the total cost cannot exceed $64,000. The company would like to maximize the minimum inventory level for all periods.

Formulate this problem as a linear programming.