You are a hotel manager and you must analyze the loss of cutlery every week. The last Friday night when his person tried to set the table for 500 people, there were not enough knives. So you need to order more cutlery, but you want to take any quantity discounts the seller offers you.

For a small order (2000 or less), the supplier sets a price of $ 1.80 / U. If you order between 2001 and 5000 pieces, the price changes to $ 1.60 / U; an order of 5001 to 10,000 pieces is priced at $ 1.40 / U plus 10,001 units thereafter priced at $ 1.25 / U.

Ordering costs are $ 200 per order, your annual inventory holding costs are 5%, and your annual demand is 45,000 pieces.

For the best alternative:

a) what is the optimal quantity to order?

b) What is the annual cost of maintaining inventory?

c) What is the annual cost of preparing?

d) What are the annual costs of the cutlery with an optimal quantity to order?

e) What is the total annual cost, which includes ordering, maintaining, and purchasing silverware?