A manufacturer fabricates various products from two basic inputs, material A and material B. Material A is used at a steady rate of 1,000 units per year and costs $200 per unit. Material B is used at a rate of 500 units per year and costs $150 per unit. The manufacturer uses a 20 percent annual holding cost rate, and the fixed cost to place an order is $50, of which $10 is the cost of placing the purchase order and $40 is the fixed cost of a truck delivery. The variable (i.e., per unit charge) trucking cost is included in the unit price. The plant runs 365 days per year.

a. Use the EOQ formula with the full fixed order cost of $50 to compute the optimal order quantities, order intervals, and annual cost for material A and B. What fraction of the total annual (holding plus order) cost consists of fixed trucking cost?

b. Using a week (7 days) as the base interval, round the order intervals for material A and B to the nearest power of 2. If you charge the fixed trucking fee only once for deliveries that coincide, what is the annual cost now?

c. Leave the order quantity for material A as in (b), but reduce the order interval for material B to match that of material A. Recompute the total annual cost and compare to part (b). Explain your result.