An automotive warehouse stocks a variety of parts that are sold at neighborhood stores. One particular part, a popular brand of oil filter, is purchased by the warehouse for $$150$ each. It is estimated that the cost of order processing and receipt is $$100$ per order. The company uses an inventory carrying charge based on a $28$ percent annual interest rate. The monthly demand for the filter follows a normal distribution with mean $280$ and standard deviation $77.$ Order lead time is assumed to be five months. Assume. that if a filteris demanded when the warehouse is out of stock, then the demand is backordered, and the cost assessed for each back$-$ordered demand is $$12\mathrm{.}80.$ Determine the following quantities:

a$.$ What policy should Bobbi use if the stock$-$out cost is replaced with a Type $1$ service objective of $95$ percent?

b$.$ What policy should Bobbi use if the stock$-$out cost is replaced with a Type $2$ service objective of $95$ percent? $($You may assume an EOQ lot size.$)$

c$.$ Find the reorder level that should be used in order to satisfy $99$ percent of customer demands for the part.