A manager of a store that sells and installs hot tubs wants to prepare a forecast for the number of hot tubs demanded during 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: yt = 70 + 6t, where t = 0 in June of last year. Seasonal relatives are 1.10 for January, 1.02 for February, and 0.95 for March. What demands should she forecast? (Round the final answers to 1 decimal place.) Month Forecast January 123.2 Numeric ResponseEdit Unavailable. 123.2 incorrect. February 120.4 Numeric ResponseEdit Unavailable. 120.4 incorrect. March 117.8 Numeric ResponseEdit Unavailable. 117.8 incorrect.
Question
A manager of a store that sells and installs hot tubs wants to prepare a forecast for the number of hot tubs demanded during 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: yt = 70 + 6t, where t = 0 in June of last year. Seasonal relatives are 1.10 for January, 1.02 for February, and 0.95 for March. What demands should she forecast? (Round the final answers to 1 decimal place.) Month Forecast January 123.2 Numeric ResponseEdit Unavailable. 123.2 incorrect. February 120.4 Numeric ResponseEdit Unavailable. 120.4 incorrect. March 117.8 Numeric ResponseEdit Unavailable. 117.8 incorrect.
Solution
To calculate the forecasted demand, we first need to calculate the trend component for each month using the given equation yt = 70 + 6t.
The value of t is the number of months since June of last year. So for January, February, and March of next year, t would be 7, 8, and 9 respectively.
For January, the trend component would be: yt = 70 + 67 = 112 For February, the trend component would be: yt = 70 + 68 = 118 For March, the trend component would be: yt = 70 + 6*9 = 124
Next, we multiply the trend component by the seasonal relatives for each month to get the forecasted demand.
For January, the forecasted demand would be: 112 * 1.10 = 123.2 For February, the forecasted demand would be: 118 * 1.02 = 120.36 For March, the forecasted demand would be: 124 * 0.95 = 117.8
So, the forecasted demands for January, February, and March are 123.2, 120.4, and 117.8 respectively.
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