### Determine the optimal reorder quantity

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An automotive repair shop stocks many sizes of tires. One particular size and model is purchased for \$15 and sold for \$30. The manager estimates the cost to order at \$75, including the delivery charge and paperwork. Using the cost of rent, interest, and utilities, the manager estimates the cost of carrying inventory at approximately 50% per year based on average inventory value. The shop sells approximately 2,000 of these tires per year. Orders are received two weeks after an order is placed.

(a) Determine the optimal reorder quantity

(b) Determine the optimal reorder point.

(c) What is the total cost associated with the optimal (Q, r) policy?

(d) What is the average time between orders?

(e) How many orders are placed per year?

(f) Suppose the repair shop orders 150 tires at a time. What is the increase in cost versus an optimal order quantity?

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