19.03.2023 - 21:22

# Sales of Volkswagen’s popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years (see table below). The sales manager had predicted before the new model was introduced th

Question:

Sales of Volkswagen’s popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years (see table below). The sales manager had predicted before the new model was introduced that first year sales would be 410 VWs. Using exponential smoothing with a weight of a 5 .30, develop forecasts for years 2 through 6.

YEAR SALES FORECAST

1 450 410

2 495

3 518

4 563

5 584

6 ?

SOLUTION YEAR FORECAST

1 410.0

2 422.0 = 410 + .3 (450 – 410)

3 443.9 = 422 + .3 (495 – 422)

4 466.1 = 443.9 + .3 (518 – 443.9)

5 495.2 = 466.1 + .3 (563 – 466.1)

6 521.8 = 495.2 + .3 (584 – 495.2

• April 12, 2023 в 03:12
Using exponential smoothing with a weight of 0.3, the forecasts for years 2 through 6 for Volkswagen's popular Beetle sales in Nevada are as follows: - Year 2: 422.0 - Year 3: 443.9 - Year 4: 466.1 - Year 5: 495.2 - Year 6: 521.8 Exponential smoothing is a forecasting technique that uses the weighted average of past observations to predict future values. The weight given to each past observation decreases exponentially as the observation gets older. In this case, the weight used is 0.3, which means that the most recent observation has a greater influence on the forecast than the older ones. To calculate the forecast, we start with the predicted value for Year 1, which was given as 410.0 by the sales manager. For Year 2, we take a weighted average of the predicted value for Year 1 and the actual sales in Year 1 (450), with the weight given to the actual sales being 0.3 and the weight given to the predicted value being 0.7 (1 - 0.3). This gives us a forecast of 422.0 for Year 2. We repeat this calculation for each subsequent year, using the forecast from the previous year and the actual sales from the current year. Overall, the forecasts show a steady increase in sales over the 5-year period, in line with the trend observed in the actual sales data.
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