A dry cleaner uses exponential smoothing to forecast equipment usage at its main plant. August usage was forecasted to be 88 percent of capacity; actual usage was 89.6 percent of capacity. A smoothing constant of .1 is used. a. Prepare a forecast for September. b. Assuming actual September usage of 92 percent, prepare a forecast for October usage.

a) 88.16%

b) 88.54%

Explanation:

a. Prepare a forecast for September.

Smoothing constant (α) = 0.1

Forecast for August (Ft) = 88%

Actual usage for August (At) = 89.6%

Forecast for September (Ft+1) =?

Ft+1= Ft+ α (At– Ft)= 88% + 0.1 (89.6 – 88)%

= 88% + 0.16%

= 88.16% is the forecasted usage for the month September.

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

Smoothing constant (α) = 0.1

Forecast for September (Ft) = 88.16%

Actual usage for September (At) = 92%

Forecast for October (Ft+1) =?

Ft+1= Ft+ α (At– Ft)= 88.16% + 0.1 (92 – 88.16)%

= 88.16% + 0.384%

= 88.54% is the forecasted usage for the month of October.