Inventory control system

A company based in Illinois has invented a way to make pepperoni out of soy beans, and this pepperoni product has developed a niche market among pizzerias in Anaheim. The owner, Mr. Bean, has asked his sister to serve as a local distributor and estimates that the demand for the pepperonis is fairly steady at 2000 per year. The pepperonis cost Mr. Bean $1.85 per unit to produce, and he is willing to sell them to his sister for $2.00. Due to their composition, the pepperonis must be kept refrigerated, so Ms. Bean has made arrangements with a trucking company for refrigerated shipments at a cost of $250 for up to 1000 pepperonis. It takes one week for Ms. Bean to receive to receive an order from the factory. Ms. Bean is financing the distributorship using her credit cards, and estimates that, between the interest on her credit cards and the cost of storage, her annual holding cost rate is 40%.
(a) How many pepperonis should Ms. Bean have trucked in at one time, and how often should she order them?
(b) When should Ms. Bean call her brother to send another shipment?
(c) Suppose that the pepperonis sell for $3.00 each. Are these pepperonis a profitable item for Ms. Bean? If so, what annual profit can she expect to realize from this item? (Assume that she uses the best inventory control system for this situation.)
(d) During the winter, the truck is sometimes delayed by snow. The trucking company has provided Ms. Bean information on actual transit times that occurred last winter. From this, Ms. Bean estimates that the demand during the actual transit time would have had a mean of 50 and a standard deviation of 20. Suggest and justify a service level that is appropriate considering the economics of this situation, and find the corresponding reorder point.

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