Ajewelry 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 cost are $48.

a. if carrying costs are $2 per year for each stone, find the order quantity that will minimize total annual cost.

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

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The returns on the common stock of maynard cosmetic specialties are quite cyclical. in a boom economy, the stock is expected to return 22 percent in comparison to 9 percent in a normal economy and a negative 14 percent in a recessionary period. the probability of a recession is 35 percent while the probability of a boom is 10 percent. what is the standard deviation of the returns on this stock?

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends > a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?