Livingston Tools, a manufacturer of battery-operated, hand-held power tools for the consumer market (such as screwdrivers and drills), has a problem. Its two biggest customers are "big box" discounters. Because these customers are fiercely price competitive, each wants exclusive products, thereby preventing consumers from making price comparisons. For example, Livingston will sell the exact same power screwdriver to each retailer, but Livingston will use packing customized to each retailer (including two different product identification numbers). Suppose weekly demand of each product to each retailer is normally distributed with mean 5,200 and standard deviation 3,800. Livingston makes production decisions on a weekly basis and has a three-week replenishment lead time. Because these two retailers are quite important to Livingston, Livingston sets a target in-stock probability of 99.9 percent.

a. Based on the order-up-to model, what is Livingston's average inventory of each of the two versions of this power screwdriver?

b. Someone at Livingston suggests that Livingston stock power screwdrivers without put- ting them into their specialized packaging. As orders are received from the two retail- ers, Livingston would fulfill those orders from the same stockpile of inventory, since it doesn't take much time to actually package each tool. Interestingly, demands at the two retailers have a slight negative correlation, 0.20. By approximately how much would this new system reduce Livingston's inventory investment?