A company packages a bulk product in bags with a 50-pound label weight. During a typical day's operation of the fill process, 22 subgroups of five bag fills are observed. Using the observed data, $ and Rare calculated to be 52.9364 pounds and 1.6818 pounds, respectively. When the 22 x's and 22 R's are plotted with respect to the appropriate control limits, the first 6 subgroups are found to be out of control. We found that the elimination of a start-up problem brought the filling process Into statistical control with T =53.5875 and R = 12937. (a) Recalling that the fill weight * and R charts are based on subgroups of size 5, and assuming that the fill weights are approximately normally distributed, calculate the natural tolerance limits for the process. (Round your answers to 4 decimal places.) Natural tolarence limits are (b) Suppose that management wishes to reduce the mean fill weight in order to save money by "giving away" less product. However, since customers expect each bag to contain at least 50 pounds of product, management wishes to leave some process leeway. Therefore, after the mean fill weight is reduced, the lower natural tolerance limit is to be no less than 51.5 lb. Based on the natural tolerance limits, how much can the mean fill weight be reduced? If the product costs $3 per pound, and if 1 million bags are sold per year, what is the yearly cost reduction achieved by lowering the mean fill weight? (Round mean answer to 4 decimal places.) The mean in weight can be reduced by pounds Annual cost reduction