PROBLEM 1: (70 marks) The Fowler Martial Arts Academy trains young boys and girls in self-defence. Joan Fowler, the owner of the academy, notes that monthly revenue is higher when school is in session but quite low when school is out (because many children are away on vacation or at summer camp). She has researched revenues for the past four years and obtained the information shown in the Table below. Answer the following questions based on the data provided in the table. Month Year 1 Year 2 Year 3 Year 4 January $59,042.00 $57,495.00 $56,583.00 $55, 658.00 February $62,659.00 562,622.00 $66,438.00 $67, 164.00 March $22,879.00 524,273.00 | $27,766.00 |$27,795.00 April $29,946.00 $30,492.00 $31,600.00 $30,667.00 May $26,839.00 $28,237.00 $29,589.00 $31,962.00 June $19,134.00 $17,893.00 $20, 115.00 $21, 096.00 July $20,051.00 $21, 126.00 $19,324.00 |$22,778.00 August $19,625.00 $22,876.00 $23,486.00 $23, 144.00 September $19,925.00 522,641.00 $24,719.00 $26,601.00 October $58, 435.00 560,796.00 $60,666.00 |$61,385.00 November $87,705.00 587,815.00 $86,693.00 $88, 581.00 December $77,430.00 $78,711.00 $80,056.00 |$81,048.00 a) Forecast the revenue for January Year 5 using the moving averages method. Consider three different numbers of periods for the moving average calculation (3, 6, and 9 months). (12 marks) 1. Do the January forecast for Year 5 change if you change the number of periods to calculate the moving average? Enumerate the three different forecasts (using the three periods) for January Year 5. (2 marks) 2. Plot both the actual and predicted revenue for all three moving average calculations (You will have four plots in total on one chart - the actual data and the three forecasts). (2 marks) 3. Visually inspect the plots for all three moving average predictions (i.e. moving averages based on 3, 6, and 9 months). a. What are the advantages of using a small number of periods in the moving average calculations? What are the disadvantages? (2 marks) b. What are the advantages of using a large number of periods in the moving average calculations? What are the disadvantages? (2 marks) 4. Which model is the best (the one based on a 3, 6, or 9 months moving average)? Why? Show your calculations. (4 marks)