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$$ less$)$ her vendor quotes a price of $$$$/$piece$.$

If she orders to $$pieces$,$ the price drops to $$$$/$piece$.$

to pieces brings the price to $$$$/$piece$,$ and

and above reduces the price to $$$$/$piece$.$

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

Part $2$

$$a$)$ What is the optimum ordering$$ quantity?