AggTech is measuring the service level through product availability. Currently they are operating with 85% product availability. Based on the historical data, their weekly demand has a standard deviation of 700 items, and the the lead time is a week. They estimated that if they change the service level by 1%, the sales would change by 0.033%. Currently, their annual revenue is $750,000. Cost of obtaining each item for AggTech is $45 and the inventory holding cost rate is 10%. Accordingly, answer the following questions: a) [4] What is the item holding cost? D = 10%, cost = 45 per item = 10/100 45 4.5 dollars per unit. b) [9] Write down the expression that calculates the marginal cost in terms of change in z score corresponding to service levels (i.e., deltaZ) Using the Z table we see that z value for 85% = 1.04 and a change of 1% = 1.00 so Deltaz 1.04-1.00 = .04 aci asl = standard deviation of items Az = 700 .04 = 28 c) [9] Calculate the marginal revenue. d) [8] What is the optimal service level? You can just provide the interval, for example, 90%-91%. For full credit, you must show your work below.