Problem:

$R$&$B$ Beverage is a distributor of beer, wine and soft drinks products. From a main warehouse in

Columbus, Ohio, R & B supplies nearly $1000$ retail stores with beverage products. The

warehouse runs its distribution trucks $7$ days a week. The warehouse manager has decided to do a

detailed study of the inventory costs associated with Bub Beer, the number$-$one$-$selling R & B

beer. She wants to determine how much to order and when to order for Bub Beer that results in

the lowest possible cost. After tracking sales for the past $10$ weeks, the sales manager can safely

assume weekly sales are about $4,000$ cases. The assumption of constant demand appears

appropriate. Considering warehouse cost, rate of return, breakage, taxes, pilferage and spoilage,

the annual inventory holding cost is about $25\%$ of the value of the inventory. $R$&$B$ pays about

$$16$ per case. The cost of placing an order includes the salary of purchasers, transportation and

receiving costs. All of those costs total about $$64$ per order regardless of the order quantity.

Questions:

She currently orders $8,000$ cases at a time. What's her average inventory level?

If she currently orders $8,000$ cases at a time, how many times a year does she place an order?

Assume $52$ weeks in a year.

If she places an order $20$ times a year, how many days between the placement of orders? Here,

assume $360$ days a year.

How many cases should the manager order at a time to minimize total annual inventory carrying

cost and ordering cost. Assume $52$ weeks per year. Round your answer to the nearest integer.

What's the total annual cost of this inventory policy? Round your answer to the nearest dollar.

Recall that Bub operates $7$ days a week. Bub Beer's supplier guarantees a $2-$day delivery on all

orders. R & B should place an order when inventory falls to cases.