You manage a factory that sells two products: A and B that are supplied by a manufacturer. The manufacturer charges a $200 fixed shipping and handling fee for each order of A or each order of B and the unit costs for A and B are $700 and $800 respectively. Demand for A and B are 250 per month and 300 per month respectively. The inventory holding cost is based on an annual interest rate of 15%. Currently you manage your inventory by calculating the EOQ for each product separately. Assume that you can round the fractional order quantity to the nearest integer.

a. What are the EOQs for A and B? What are the annual setup and holding costs for A and B?

b. Currently the store has a storage constraint that it can only hold 60 units of A and 75 units of B. What will be the optimal order quantities for A and B? What will be the resulting annual setup and holding costs? (Assume that the space for A cannot be used for B and vice versa.)

You wonder if calculating two separate EOQs is too cumbersome and considering ordering both A and B at the same time. That is whenever you place an order, you could order both A and B. The manufacturer charges a $400 shipping and handling fee for any sized order. Solve the following 2 parts based on this setting. (Assume no storage constraint.)

c. Let T denote time between successive orders. What will be the optimal T if you want to minimize the total setup and holding cost? What are the corresponding order quantities?

d. What is the resulting total setup and holding cost? How does it compare to the cost in part 1 when you order A and B separately? Explain why.