Problem $12-14($Algo$)$

A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $$8\mathrm{.}10$ per stone for

quantities of $600$ stones or more, $$8\mathrm{.}50$ per stone for orders of $400$ to $599$ stones, and $$9\mathrm{.}00$ per stone for lesser quantities.

The jewelry firm operates $260$ days per year. Usage rate is $18$ 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.

Note: 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.

Optimal order quantity

b$.$ If annual carrying costs are $30$ percent of unit cost, what is the optimal order size?

Note: 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.

Optimal order quantity

c$.$ If lead time is $3$ working days, at what point should the company reorder?

Note: Do not round intermediate calculations. Round your final answer to the nearest whole number.