A wine importer sells on average 450 cases a week of a particular wine. The importer currently buys the wine at a cost of $78 per case. The importers cost of capital is 25% per year, that is, the cost of holding one unit in stock is 25% of its value. Each order placed with the winery costs the importer $150. This cost includes labor, forms, record keeping for tax purposes etc. (The winery pays for shipping.)

(a) [3 points] What order quantity minimizes the importers total inventory-related costs (i.e., holding and ordering costs)? What are the importers annual inventory- related costs given this order quantity? (Assume a 52-week year.)

(b) [2 points] Inventory turnover is a measure of the number of times inventory is sold or used in a time period such as a year. It equals the purchasing cost of goods sold divided by the average inventory value. What is the inventory turnover per year of this wine?

(c) [3 points] In reality, there is some variation in the importers weekly demand. Weekly demand is approximately normally distributed with a standard deviation of 140 cases. After the importer orders from the winery, it takes seven weeks to receive the order. To ensure that the importer does not run out of stock during the seven-week lead time, instead of placing a new order each time the inventory level reaches zero, the importer needs to have certain amounts of inventories on hand (called reorder point) when placing the order. If the importer wishes to provide a 95% service level to its customers, what is the reorder point?