(a) A Toyota plant at the East Coast region of US would want to forecast demand for its Toyota Corolla car next year using the data for the past four years shown in the table below. A related problem is the number of tires that must be ordered for the forecasted car demand which includes one spare tire for each car. The plant has secured a contract for 100,000 tires for 2023. However, in case the number of tires required for the forecasted demand for a year exceeds the contracted value, it may have to trigger for a so-called "orphanage' scheme from the parent per car. The orphanage scheme however must be triggered at the beginning of the year. company to make up for the shortfall to avoid possible lost sales which is estimated at US$2500 Production of Toyota Corolla (in 1000s) Quarter 1 Quarter 2 Quarter 3 Year Period 1 4.8 Quarter 4 2019 42 6.4 5.8 6.6 2020 -53 6.9 7.7 6.1 2021 5.6 7.17 8.1 6.4 2022 5.9 8.4 9.1 Let S, and SF, be the seasonal factor and seasonally adjusted demand forecast for quarter i, i = 1,2,3,4, and F, the demand forecast for period t, t = 1,2,3,4 1812 i. Develop a seasonally adjusted forecast model for demand for Corolla cars using the data in the table above. (2 marks) ii. Forecast demand for each quarter for 2023 (using a linear trend line forecast estimate for orders in 2023). (6 marks) iii. What is the number of car tires needed to meet the forecasted demand for each quarter in 2023? (2 marks) iv. Would the plant have to trigger the orphanage scheme? Explain. (2 marks) v. Suppose the Toyota plant decides not to trigger the orphanage scheme, how much money would the plant loose due to lost sales? (2 marks) Mir