ACold$)$ ACold Inc. is a frozen food distributor with $10$ warehouses across the country Iven Tory, one of the warehouse managers, wants to make sure that the inventory policies used by the warehouse are minimizing inventory while still maintaining quick delivery

to ACold$$s customers. Since the warehouse carries hundreds of different products, Iven

decided to study one. He picked Caruso$$s Frozen Pizza $($CFP$).$ Demand for CFPs averages

$400$ per day with a standard deviation of $200.$ Weekly demand $($five days$)$ averages $2,000$

units with a standard deviation of $555.$ Since ACold orders at least one truck from General

Foods each day $($General Foods owns Caruso$$s Pizza$),$ ACold can essentially order any

quantity of CFP it wants each day. In fact, ACold$$s computer system is designed to imple$-$

ment a base stock policy for each product. Iven notes that any order for CFPs arrives four

days after the order. Further, it costs ACold $$0\mathrm{.}01$ per day to keep a CFP in inventory, while

a back order is estimated to cost ACold $$0\mathrm{.}45.$

a$.$ What base stock level should Iven choose for CFPs if his goal is to minimize holding

and back$-$order costs? $[16\mathrm{.}7]$

b$.$ Suppose the base stock level $2,800$ is chosen. What is the average amount of inventory

on order? $[16\mathrm{.}5]$

c$.$ Suppose the base stock level $2,800$ is chosen. What is the annual holding cost? $($Assume

$260$ days per year.$)[16\mathrm{.}5]$

d$.$ What base stock level minimizes inventory while maintaining a $97$ percent in$-$stock

probability? $[16\mathrm{.}6$