10) A large seller of high-end mountain bikes has three retail outlets throughout the San Francisco Bay Area. Weekly demand at each outlet is normally distributed, with means of 250,320 , and 410 bikes. The standard deviations are 50,30 , and 45 , respectively. The lead-time for replenishment from the manufacturer is 2 weeks. Each outlet covers a separate geographic area (assume there is no demand correlation between the areas). These high-performance bikes cost the retailer $2,000 dollars each. Inventory holding costs are estimated at 20% of the item value. a. Determine the required level of safety stock at each location for an 85%,90%, 95%, and 99% service levels. What is the total cost of SS at each location? What is the total cost of the safety inventory for the entire chain (for each scenario)? How would you describe the relationship between service level and total safety stock cost? b. Assuming a 90% service level, what would be the effect on safety stock if the three outlets were consolidated into one large outlet (aggregated)? Would there be any savings (in terms of the cost of the inventory and holding cost)? c. Assume they aggregated as suggested in part (b). What is the reorder point? d. Assume they aggregated as suggested in part (b). If every time they place an order they receive a shipment of 2500 bikes, what is the total annual holding cost of inventory? Hints: i) the mean of the sum of multiple random variables is the sum of their individual means; ii) the variance of the sum of multiple independent random variables is the sum of their independent variances