The daily demand for an item is distributed normally, with a mean of 5 and a variance of 2. The cost to place an order is $10, and the carrying charge per day is estimated at 10 percent of the inventory value. The supplier has offered the following purchase plan:
a. Recommend an optimal order quantity that will minimize the total inventory costs of ordering and holding plus the purchase cost of the units. Although it is not necessary, you may assume 360 days a year.
b. Determine the reorder point and safety stock that will achieve a 95 percent service level given a constant 2-day delivery lead time. Assume daily demand is an independent variable.