Problem 4. (Probabilistic Inventory Model. Total 15pts.) The SmartAuto is a car dealer that sells new cars. Customer Demands and Order Delivery Time from the car manufacturer may vary randomly from time to time. Assume that historical data shows that the Demand During Delivery Lead-time can be summarized in the following table. Assume that SmartAuto can sell on average 1000 cars a year, and the manager currently orders 200 cars each time from the manufacturer whenever its inventory drops to 12 . a. Calculate i. The Safety stock kept = ii. the Chance of Stockout, and the Service level. iii. the Expected number of shortages that may incur within Each Ordering Cycle. b. Assume that it will cost the firm $200 to hold a car in inventory for a year; and will cost the firm additional $150 on service for each car that has to be backordered due to shortage. Find the optimal Reorder Point (or Safety Stock) such that the Total Costs in keeping Safety Stock and on Shortage are minimized. (hint: use Excel spreadsheet since it can help to save calculation time significant)