Daily demand for a certain product is normally distributed with a mean of 60 and a standard deviation of 7. The source of supply is reliable and maintains a constant lead time of 3 days. The cost of placing the order is $10, and the annual holding costs are $0.50 per unit. Sales are not lost when there is a stockout and unfilled orders are filled as soon as the next order arrives, albeit with a cost of lost goodwill of $0.35 per unit. The selling price and purchase cost for the product are $5 per unit and $2 per unit, respectively. Assume that sales occur over the entire 365 days of the year.

Suppose the firm uses a periodic review policy and inventory is reviewed every 7 days. And there is no lead time. 1. Find the order-up-to level (OUL) that results in a cycle service level of 95%. [20 points] 2. If there are 200 units in stock at the time of the current inventory review, how many units should be ordered (i.e., what is the order size)? [10 points]