$9.$ A retailer has four store locations A$,$ B$,$ C$,$ and D$.$ Each store orders from an external supplier based outside the city. Table $1$ contains information about the daily demand at each location and the monthly rental cost. Each store uses a periodic review model. They order once in $10$ days, the product is received $2$ days later, and the service level is $99\%.$ The retailer wants to consolidate by closing the $4$ stores and opening a new store at a central location E$.$ The estimated demand at location E and the rental cost is also in Table $1.$ The new location will continue to order once in $10$ days, the lead time will remain $2$ days, and the service level will continue at $99\%.$

Location Daily Demand Average Standard Deviation of Daily Demand Rental Cost $($Monthly$)$

A $10060$ $$3,600$

B $200100$ $$4,800$

C $300120$ $$6,000$

D $7550$ $$3,600$

E $660160$ $$11,400$

Transportation costs from the supplier to the store are approximately the same for each of the $5$ locations $($A$,$ B$,$ C$,$ D$,$ and E$)$ at $$0\mathrm{.}25/$ Unit. The retailer purchases each unit for $$50$ and sells for $$75.$ Cost of holding a unit in inventory is $$2/$ month. The retailer expects to save $$7,500/$ month in overhead and labor costs by reducing the number of locations. Assume that there are $30$ days in a month.

a$.$ What is the average inventory level at Store A$?$