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 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 $$\frac{1\mathrm{.}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 $$205$ per order, her annual holding costs are $5\%,$ and the annual demand is $49,600$ 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$).$