A company has to organize its aggregate production schedule for the next 3 months. Units may be produced on regular time or overtime. The relevant costs and capacities are shown in Table 5 below. TABLE 5 MANUFACTURING DATA Capacity Production Costs Period Regular Time Over Time Regular Time Over Time Demand 1 120 2 90 225 16 20 70 12 18 21 90 3 80 18 18 24 150 There is 1 cost per unit of inventory held, and the inventory at the beginning of the 2 months is equal to 15 units. Also, sales can be backordered at a cost of 2 per unit a month. Backorders occur when demand is temporarily out of stock, and it will be satis- fied with future production at an additional cost.

a. Identify the objective function with total costs to minimize.

b. Identify and formalize in Excel the various constraints.

c. Build in Excel, using the Simplex LP Solver the optimal production schedule.