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Speedy Wheels is a wholesale distributor of bicycles. Its Inventory Manager, Ricky Sapolo, is currently reviewing the inventory policy for one popular model that is selling at the rate of 500 per month. The administrative cost for placing an order for this model from the manufacturer is $1,000 and the purchase price is $400 per bicycle. The annual cost of the capital tied up in inventory is 15 percent of the value (based on purchase price) of these bicycles. The additional cost of storing the bicycles—including leasing warehouse space, insurance, taxes, and so on—is $40 per bicycle per year.

(a) Use the basic EOQ model to determine the optimal order quantity and the total variable inventory cost per year.

(b) Speedy Wheel’s customers (retail outlets) generally do not object to short delays in having their orders filled. Therefore, management has agreed to a new policy of having small planned shortages occasionally to reduce the variable inventory cost. After consultations with management, Ricky estimates that the annual shortage cost (including lost future business) would be $150 times the average number of bicycles short throughout the year. Use the EOQ model with planned shortages to determine the new optimal inventory policy.