tried to set up for a banquet for $500$ people, they did not have enough knives. She decides she needs to order some more silverware, but wants to take advantage of any quantity discounts her vendor will offer.

$>$ For a small order pieces or less$)$ her vendor quotes a price of $$1,\frac{80}{?}$ piece.

$>$ If she orders $2,001$ to $5,000$ pieces, the price drops to $$\frac{1\mathrm{.}60}{?}$ piece.

$>5,001$ to $10,000$ pieces brings the price to $$\frac{1\mathrm{.}40}{?}$ piece, and

$>10,001$ and above reduces the price to $$\frac{1\mathrm{.}25}{?}$ piece.

Lisa's order costs are $$200$ per order, her annual holding costs are $5\%,$ and the annual demand is $48,800$ pieces. For the best option $($the best option is the price level that results in an EOQ within the acceptable range$)$:

a$)$ What is the optimum ordering quantity? units $($round your response to the nearest whole number$).$

b$)$ What is the annual holding cost? $ $($round your response to two decimal places$).$

c$)$ What is the annual ordering cost? $ $($round your response to two decimal places$).$

d$)$ What are the annual costs of the silverware itself with an optimal order quantity? $ $($round your response to the nearest whole number$).$

e$)$ What is the total annual cost, including ordering, holding, and purchasing the silverware? $($round your response to two decimal places$).$