A dry cleaner uses exponential smoothing to forecast equipment usage. The August forecast was 88% and the actual was 89.6%. Use a smoothing constant of 0.1. A. Prepare a forecast for September.
B. Assuming actual September usuage of 92 %, prepare a forecast for October usage

1. 88.16%

2. 88.54%

Explanation:

a. Prepare a forecast for September

Smoothing constant (a) is 0.1

Forecast for August (Ft) is 88%

Actual usage for August (At) is 89.6%

Forecast for September(Ft +1) will therefore be;

Using the formulae

= Ft+a (At-Ft)

= 88% + 0.1(89.6% - 88%)

= 88% + 0.16%

= 88.16%

b. Assuming actual September usage of 92% , prepare a forecast for October usage.

Since we have the following,

Smoothing constant(a) 0.1

Then forecast for September(Ft) is 88.16%

Also, actual usage for September (At) is 92%

Therefore, forecast for October (Ft + 1) will be,

Using the formula

= Ft+a(At - Ft)

= 88.16% + 0.1(92% - 88.16%)

= 88.16% + 0.384%

= 88.54%