Darrin owns a company that sells and installs hot tubs: sales are fairty consistent from year to year. The table below shows average sales per month for the previous year. Average Sales per Month Month October November December January February March April 550 450 600 850 925 675 500 Based on last year's data, calculate the forecasts for average sales per mnonth for Jaruary- April, using the different methods below. a) Calculate the simple 3-month moving average forecast for January - April. (6 points) b) Calculate the weighted 3-month moving average for January - April using weights of o.55, 0.30, and o.15 (highest weight for the most recent periodj. (6 points) c) Calculate the single exponential smoothing forecast for January - April using an initial forecast (F) for October of 500, and an a of o.45- (8 points) d) Determine the equation of the linear trend line based on the data from October - April; indicate the forecast for January-April. (o points) e) Calculate the trend-adjusted exponential smoothing forecasts for January - April using an initial trend forecast (T) for October of so, and initial exponential smoothing forecast (S.) for October of 5o0; also, use an a of 0.35 and a of o.50. (10 points) ) Calculate the Mean Squared Error (MSE) for the forecasts made by each technique in January - April. Based on MSE, which forecasting method is preferred? Using the preferred technique forecast the average sales per month for the following z months (May and June). (10 points)