Problem $12-14($Algo$)$

A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $$8\mathrm{.}30$ per stone for quantities of $600$ stones or more, $$8\mathrm{.}70$ per stone for orders of $400$ to $599$ stones, and $$9\mathrm{.}20$ per stone for lesser quantities. The jewelry firm operates $180$ days per year. Usage rate is $35$ stones per day, and ordering costs are $$40.$

a$.$ If carrying costs are $$3$ per year for each stone, find the order quantity that will minimize total annual cost. $($Do not round intermediate calculations, except for order quantities which should be rounded to the nearest whole number. Round your final answer to the nearest whole number.$)$ b$.$ If annual carrying costs are $25$ percent of unit cost, what is the optimal order size? $($Do not round intermediate calculations, except for order quantities which should be rounded to the nearest whole number. Round your final answer to the nearest whole number.$)$ c$.$ If lead time is $4$ working days, at what point should the company reorder? $($Do not round intermediate calculations. Round your final answer to the nearest whole number.$)$