$6.$ Consider an item whose inventory is controlled by a periodic review, base$-$stock policy. Suppose the review period is $7$ days, the replenishment lead$-$time is $3$ days, and the daily demand is normally distributed with mean $10$ and standard deviation $4.$

a$.$ Suppose we set the target $($base stock$)$ level at $130.$ What is the coverage probability? What is the average inventory level?

b$.$ Suppose we have two categories of customers $$ gold and silver. We promise a higher level of service to the gold customers $($e$.$ g$.,99\%$ of demand is satisfied from stock$)$; for silver customers, the service level would be lower, e$.$ g$.,85\%$ of demand satisfied from stock. Describe how you might manage the inventory to serve the two demand classes? $($We don$$t expect you to find a specific policy, but you should attempt to describe conceptually how you might structure a policy and then operate with this policy$).$