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 $(2,000$ 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.

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