Forecasting and Inventory Management with Uncertainty (27 points). A commerce student is starting a summer intern position at Joe's tire store. The student aims to improve the inventory management policy at the store. As a first step, the student checks the historical demand data, which is shown below. The store's forecasted demand is also available. Year (t) Sales Forecasts 1 600 600 2 800 600 3 920 660 4 1000 738 Question 14 4 pts A) The store manager applied the exponential smoothing method to generate the forecasted demand. What smoothing constant (a) has been used? Question 15 3 pts B) Compute the mean absolute deviation (MAD) of the used forecasting method for years 1-4. Question 16 3 pts C) Suppose the manager wants to stick with the exponential smoothing method, would you pick a larger value of a to improve the forecasting performance? Why or why not? Based on the historical demand, the student estimates the expected annual demand rate to be 830 with a standard deviation of 174. The store manager checks the inventory of tires every 9 weeks and the lead time is 4 weeks (assume a year has 52 weeks). Suppose currently there are 100 tires in stock. Question 17 8 pts D) If the manager wants to target a 90% in-stock probability, how many tires should be ordered at this time? Round your answer to a whole number (the nearest integer, for example, 2.52 should be rounded to 3, and 2.42 should be rounded to 2). Question 18 4 pts E) The manager is considering upgrading the inventory management system so the inventory level can be tracked continuously. With this upgrade, how much safety stock does the store need to carry to maintain a 90% in-stock probability? Round your answer to a whole number (the nearest integer, for example, 2.52 should be rounded to 3, and 2.42 should be rounded to 2). Question 19 5 pts F) The student is asked to plan a sales event for the upcoming winter season. All winter tires must be ordered in August and can not be replenished during the winter. Each winter tire comes with a purchase cost of $60. The leftover winter tires at the end of the season will be resold to the tire factory for $40 each. Suppose the newsvendor model is used to determine the optimal order quantity. Using the newsvendor formula, the student finds the critical ratio to be 0.75. What is the corresponding selling price of the winter tire (that justifies the critical ratio of 0.75)? Round your answer to two decimal places