Question: (Beer Distributor: optimal order size & discount) [25%] . A beer distributor finds that it sells on average 100 cases a week of regular 12-oz. Budweiser. For this problem, assume that demand occurs at a uniform rate over a 50-week year. The distributor currently purchases beer every two weeks at a cost of $8 per case. The inventory holding cost (capital, insurance, etc.) for the distributor equals 25 percent of the purchasing cost of the item per year. Each order placed with the supplier costs the distributor $10. This cost includes labor, forms, postage, and so forth.

1. Assume the distributor can choose any order quantity it wishes. What order quantity minimizes the distributor’s annual inventory-related costs defined as the sum of carrying and ordering costs)?
   For the next three sub-questions, assume the distributor selects the order quantity specified in part (a).
2. What is the distributor’s inventory turns per year?
3. What is the distributor’s annual inventory-related cost? What is the average inventory-related cost per case of beer sold?
4. Suppose the brewer is willing to give a 5 percent quantity discount (so that unit cost is reduced to $7.6) if the distributor orders 600 cases or more at a time. If the distributor is interested in minimizing its total cost (i.e., purchase and inventory-related costs), should the distributor begin ordering 600 or more cases at a time?

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