Problem $3.($Chapter $9$: Inventory Policy Decisions$)$ Suppose that an auto part in a manufacturers inventory has the following characteristics: $------------------------------------------------------------$ Forecast of demand $=900$ cases per week Forecast error, std$.$ dev. $=125$ cases per week Lead time $=4$ weeks Carrying cost $=30\%$ per year Purchase price, delivered $=$ $$60$ per case Replenishment order cost $=$$$40$ per order Stockout cost $=$$$10$ per case Probability of being in stock during the lead time $=85\%-------------------------------------------------------------$ The manufacturer uses ROP method to control the inventory of this item. The manufacturer operates $52$ weeks a year. a$.$ What is the economic order quantity? b$.$ What is the reorder point? c$.$ Whats the expected number of units out of stock annually? d$.$ What is the annual service level? e$.$ Whats 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 $0\mathrm{.}5$ weeks, whats the ROP?