Question

A manager of a store that sells and installs spas wants to prepare a forecast for January, February, and March of next year. Her forecasts are a combination of trend and seasonality. She uses the following equation to estimate the trend component of monthly demand: Ft = 90 + 3t where t-O in June of last year. Seasonal relatives are 1.00 for January 96 for February, and .95 for March, what demands should she predict? (Round your answers to 2 decimal places.) Month January of the next year February of the next year March of the next year Forecast

Answer 1

To calculate the forecast for each of the month, we need to find the trend component for each of the month and multiple by the trend component by the seasonal relatives to get the forecast

It is given that for June if last year t=0, hence for each of the successive month we need to increment t by 1. Thus for last year's July t=1, last year's August t=2. Following this logic we the below values of t for the months till next years January, February and March

Month June, last year July, last year August, last year September, last year October, last year November, last year December, last year January, present year February, present year March, present year April, present year May, present year June, present year July, present year August, present year September, present year October, present year November, present year December, present year January, next year February, next year March, next year Value oft 0 4 8 9 10 12 13 14 15 16 17 18 19 20 21

Thus we can see that for next year's January, February and March the values of t are 19, 20 and 21 respectively

To get the trend component for each of this month we substitute these values of t in the trend forecast 90+3t

Thus for January, trend forecast = 90+3*19 = 147

Thus for February, trend forecast = 90+3*20 = 150

Thus for March, trend forecast = 90+3*21= 153

To get the final forecasted demand we need to multiply the trend forecast above with the respective seasonal relatives

Thus for January of the next year, demand predicted = 147*1 = 147.00

Thus for February of the next year, demand predicted = 150*0.96 = 144.00

Thus for March of the next year, demand predicted = 153*0.95 = 145.35