A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $$8$ per stone for quantities of $600$ stones or more, $$9$ per stone for orders of $400$ to $599$ stones, and $$10$ per stone for lesser quantities. The jewelry firm operates $200$ days per year. Usage rate is $25$ stones per day, and ordering costs are $$48.$

a$.$ If carrying costs are $$2$ per year for each stone, find the order quantity that will minimize total annual cost. $($Round your intermediate calculations and final answer to the nearest whole number.$)$

Order quantity

stones

b$.$ If annual carrying costs are $30$ percent of unit cost, what is the optimal order size? $($Round your intermediate calculations and final answer to the nearest whole number.$)$

Optimal order size

stones