7. A firm is managing its inventory system using order-up-to policy, and orders every day. For the first 100 days, truck transportation is used and the lead time is 2 days. The corresponding order-up-to level is 150. On the 96th day, the firm orders 45; on the 97th day, the firm orders 50. (a) Consider a case that the manager thinks that truck transportation is too expensive. Thus, starting from the order of the 101st day, train transportation is used and the lead time becomes 3. Correspondingly, the order-up-to level is changed to 200. Fill in the following form: (5 points) Beginning of Day 98 99 100 101 102 103 104 105 Inventory Level 5 On-Order 45+50 Inventory Inventory Position Order Receive Demand 42 44 45 50 41 43 46 47 (b) Consider a case that the manager thinks that truck transportation is too slow. Thus, starting from the order of the 101st day, air transportation is used and the lead time becomes 1. Correspondingly, the order- up-to level is changed to 110. Fill in the following form: (5 points) Beginning of Day 98 99 100 101 102 103 104 105 Inventory 5 Level On-Order 45+50 Inventory Inventory Position Order Receive Demand 42 44 45 50 41 43 46 47 (c) Suppose that the demand for each day follows a normal distribution with mean 45 and standard deviation 3. What is the service level for the first 100 days? What is the service level after the 101st day for (a)? What is the service level after the 101st day for (b)? (5 points)