The catering manager of LaVista Hotel, Lisa ferguson, is disturbed by the amount of silverware she is losing every week. Last Friday night, when her crew tried to set up for a banquet of 500 people, they did not have enough knives. She decides she needs to order more silverware, but wants to take advantage of any quantity discounts her vendor will offer. For a small order (2000 or fewer pieces) her vendor quotes a price of $1.80 per piece. if she orders 2001-5000 pieces, the price drops to $1.60 per piece. 5001-10000 pieces are $1.40/piece, and orders of 10001 or more pieces are $1.25/piece. Lisa's order costs are $50 per order, her annual holding costs are 30%, and annual demand is 45000. For the best option,

a) what is the optimal order quantity?

b) what is the annual holding cost?

c) what is the annual ordering (setup) cost?

d) what are the annual costs of the silverware itself with an optimal order quantity?

e) what is the total annual cost, including ordering, holding, and purchasing the silverware?