K-grocery chain's logistics manager is attempting to set the customer service level (in-stock-probability) for one particular service-sensitive product item. After determining the sales-service relationship, the manager estimates that a 0.17% change in total revenue would occur for each 1% change in the in-stock probability (one major aspect of customer service). Annual sales for the item are about 100,000 cases, or 3,846 cases biweekly. The product cost in inventory is about $10/case, to which $1.3/case is added to the profit margin. Inventory carrying cost (rate) is 33% per year of item value. Stock replenishment Lead Time (LT) is about two weeks, resulting a Standard Deviation of Demand During LT about 400 cases (demand assumed approximately normally distributed). (a) Based on your analysis, what is, P, the marginal profit contribution from 1% increase of customer service level? (b) Based on the description above and your analysis in Excel (please see example Excel file from our lecture notes or your In-Class-Exercise), at the optimal service level, what z (delta z), the marginal change in safety factor are we looking for, approximately? (c) Based on the description above and your analysis in Excel, approximately what optimal service level (in-stock-probability) should the manager set? (d) What are the critical assumptions used in this decision analysis? Why?