1. A large law firm uses an average of 40 boxes of copier paper a day. The firm operates 260 days a year. Storage and handling costs for the paper are $30 a year per box, and it costs approximately $60 to order and receive a shipment of paper.
a) What order size would minimize the sum of annual ordering and carrying costs?
b) Compute the total annual cost using your order size from the previous part.
c) Except for rounding, are annual ordering and carrying costs always equal at the EOQ?
d) The office manager is currently using an order size of 200 boxes. The partners of the firm expect the office to be managed “in a cost-efficient manner”. Would you recommend that the office manager use the optimal order size instead of 200 boxes? Justify your answer.
2. Re-solve the previous problem, the first two parts, under a $10 fixed cost of ordering (S). Repeat for S = 20, 30, 40, . . . , 100. Explain in a short paragraph or two, what happens to the optimal order quantity, the time between orders, and the average inventory as S decreases.