A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.30 per stone for quantities of 600 stones or more, $8.70 per stone for orders of 400 to 599 stones, and $9.20 per stone for lesser quantities. The jewelry firm operates 102 days per year. Usage rate is 20 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.
b. If annual carrying costs are 22 percent of unit cost, what is the optimal order size?