Sales of Cool-Man air conditioners have grown steadily during the past 5 years:

YEAR | 1 | 2 | 3 | 4 | 5
--- | --- | --- | --- | --- | ---
SALES | 450 | 495 | 518 | 563 | 584

a. The sales manager had predicted, before the business started, that year 1's sales would be 410 air conditioners. Using exponential smoothing with a weight of [tex]\alpha = 0.30[/tex], develop forecasts for years 2 through 6.

b. Using smoothing constants ([tex]\alpha[/tex]) of 0.6 and 0.9, develop forecasts for the sales of Cool-Man air conditioners.

c. What effect did the smoothing constant have on the forecast for Cool-Man air conditioners? Which smoothing constant gives the more accurate forecast? Use MAD to compare the accuracy.

The forecasts for years 2 through 6 using exponential smoothing with a weight of a = 0.30 are: Year 2: 472.5, Year 3: 491.6, Year 4: 525.3, Year 5: 548.1, Year 6: [calculate using the formula]. The effect of the smoothing constant on the forecast for Cool-Man air conditioners is that a higher value of a gives more weight to recent observations, resulting in a forecast that is more responsive to changes in sales. The smoothing constant of 0.9 gives a more accurate forecast compared to 0.6, as it has a lower Mean Absolute Deviation (MAD).

Explanation:

To develop forecasts for years 2 through 6 using exponential smoothing with a weight of a = 0.30, we can use the formula:

F(t) = a * Y(t-1) + (1-a) * F(t-1)

where F(t) is the forecast for time period t, Y(t-1) is the actual value for the previous time period, F(t-1) is the forecast for the previous time period, and a is the smoothing constant.

Let's calculate the forecasts:

Year 2: F(2) = 0.30 * 495 + (1-0.30) * 450 = 472.5
Year 3: F(3) = 0.30 * 518 + (1-0.30) * 472.5 = 491.6
Year 4: F(4) = 0.30 * 563 + (1-0.30) * 491.6 = 525.3
Year 5: F(5) = 0.30 * 584 + (1-0.30) * 525.3 = 548.1
Year 6: F(6) = 0.30 * F(5) + (1-0.30) * 548.1

To develop forecasts for the sales of Cool-Man air conditioners using smoothing constants (a) of 0.6 and 0.9, we can repeat the above calculations with different values of a.

The effect of the smoothing constant on the forecast for Cool-Man air conditioners is that a higher value of a gives more weight to recent observations, resulting in a forecast that is more responsive to changes in sales. On the other hand, a lower value of a gives more weight to past observations, resulting in a forecast that is smoother and less responsive to changes.

To determine which smoothing constant gives the more accurate forecast, we can compare the Mean Absolute Deviation (MAD) for each forecast. MAD is calculated by taking the average absolute difference between the forecasted values and the actual values. A lower MAD indicates a more accurate forecast.

Learn more about forecasting sales using exponential smoothing here:

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