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 + 6t, where t = 0 in June of last year. Seasonal relatives are 1.07 for January, .88 for February, and .96 for March. What demands should she predict? (Round your answers to 2 decimal places.)Month ForecastJanuary of the next year February of the next year March of the next year

Answer 1

January = 204 x 1.07 = 218.28

February= 210 x 0.88 = 184.8

March= 216 x 0.96 = 207.36

Step-by-step explanation:

The question is to help the Manager of as store to predict sales for 3 months (January, February and March) the next year based on given estimates.

First, What is the equation for estimating the monthly demand

= Ft = 90 + 6t,

where t = 0 in June of last year

Second, what is the seasonal relatives for the three months:

January = 1.07

February = 0.88

March = 0.96

Since, t = 0, June of last year, then we calculate t for January, February, March of next yer

June to December = 6 months + 12 Months ( January to December of current year ) = 18 Months

This means that t in January = 19, February = 20 and March = 21

Finally, Calculate the trend analysis as follows

January = F19 = 90 + 6 (19) = 204

February= F20 = 90 + 6 (20) = 210

March= F21 = 90 + 6 (21) = 216

The seasonal relatives for corrected demands will be:

January = 204 x 1.07 = 218.28

February= 210 x 0.88 = 184.8

March= 216 x 0.96 = 207.36

Answer 2

A seller and installer of spas wants to forecast the requirement for January. February and March next year.

The equation to estimate the trend component of the monthly demand is:

`F_(t) = 90 + 6t`

t = 0 in June of last year.

The seasonal relatives are 1.07 for January, 0.88 for February and 0.96 for March.

If t = 0 in June last year, the value of t will be 19, 20 and 21 for next year January, February and March respectively.

Therefore using this we get the trend forecasts for:

January =
`F_(19) = 90 + 6 * 19 = 204`

February =
`F_(20) = 90 + 6 * 20 = 210`

March =
`F_(21) = 90 + 6 * 21 = 216`

The demands corrected for seasonal relatives would be::

January = 204 x 1.07 = 218.28 or 218 spas

February = 210 x 0.88 = 184.8 or 185 spas

March = 216 x 0.96 = 207.36 or 207 spas