Problem 3. (Chapter 9: Inventory Policy Decisions) Suppose that an auto part in a manufacturer's inventory has the following characteristics: Forecast of demand Forecast error, std. dev. Lead time Carrying cost Purchase price, delivered -900 cases per week -125 cases per week - 4 weeks -30% per year $60 per case Replenishment order cost =$40 per order Stockout cost -$10 per case Probability of being in stock -85% during the lead time The manufacturer uses ROP method to control the inventory of this item. The manufacturer operates 52 weeks a year. 3. What is the economic order quantity? b. What is the reorder point? c. What's the expected number of units out of stock annually? d. What is the annual service level? e. What's the total annual cost including annual fixed ordering cost, inventory holding cost, and stockout cost? f. If the lead time is normally distributed with a standard deviation of 0.5 weeks, what's the ROP?