Question

A​ check-processing center uses exponential smoothing to forecast the number of incoming checks each month. The number of checks received in June was 40 ​million, while the forecast was 42 million. A smoothing constant of 0.20 is used. ​a) Using exponential smoothing and given alpha​, the forecast for the month of July​ = nothing million checks received ​(round your response to one decimal​ place). ​b) If the​ check-processing center received 45 million checks in the month of​ July, then using exponential smoothing and given alpha​, the forecast for the month of August​ = nothing million checks received ​(round your response to one decimal​ place).

Answer 1

a. 41.6 million

b. 42.28 million

Step-by-step explanation:

A) GIven

forecast in june = Sjune = 42 million

Checks recived in june = Xjune = 40 million

Smoothing constant = a = 0.2

So for july

Sjuly = a*Xjune + (1-a)*Sjune

=0.2*40 + (1-0.2)*42 million

=8+33.6 = 41.6 million

B) forecast in july = Sjuly = 41.6 million

Checks recived in july = Xjuly = 45 million

Smoothing constant = a = 0.2

So for August

Saugust = a*Xjuly + (1-a)*Sjuly

=0.2*45 + (1-0.2)*41.6 million

=9+33.28 = 42.28 million

Note: This uses an exponential smoothing to forecast the results, but from the number of checks recived we see that it increases linearly. So we need a linear forecasting method .