use operation research method

8. Aggregate Planning Problem A company wants a high-level, aggregate production plan for the next 6 months. Projected orders for the company's products are listed in Table 3. Over the 6-month period, units may be produced in one month and stored in inventory to meet demand at some later time. Because of seasonal factors, the cost of production is not constant, as shown in the table. The cost of holding an item in inventory is $4 per unit per month. Items produced and sold in the same month are not placed in the inventory. The maximum number of units that can be stored is 250 . The initial inventory level at the beginning of the planning horizon is 200 units; the final inventory level at the end of the planning horizon is to be 100 units. Construct a mathematical program that determines the optimal amount to produce in each month so that demand is met while minimizing total production cost and inventory holding cost. Shortages are not permitted