A bicycle components warehouse stocks a variety of items that are sold at local bike shops. One particular item, a Bontrager bottle cage, is purchased by the warehouse for $1.50 each. It is estimated that the cost of order processing and receipt is $100 per order. The company uses an inventory carrying charge based on a 28% annual interest rate. The monthly demand for the bottle cage follows a normal distribution with a mean of 280 and a standard deviation of 77. Order lead time is assumed to be five months. Assume that if a bottle cage is demanded when the warehouse is out of stock, then the demand is backordered, and the cost assessed for each backordered demand is $12.80. Determine the following quantities:
1. The optimal values of the order quantity and the reorder level.
2. The average annual cost of holding, setup, and stock-out associated with this item, assuming that an optimal policy is used. a. b.