Please answer the following question correctly A dry cleaner

Please answer the following question correctly:

A dry cleaner uses exponential smoothing to forecast equipment usage at its main plant. August usage was forecasted to be 45 percent of capacity; actual usage was 56 percent of capacity. A smoothing constant of .20 is used a. Prepare a forecast for September. (Round your final answer to 2 decimal places.) Forecast for September percent of capacity b. Assuming actual September usage of 63 percent, prepare a forecast for October usage. (Round your answer to 2 decimal places.) Forecast for October percent of capacity

Solution

Forecast as per exponential smoothing:

This can be written as:

St+1=St+t,

where t is the forecast error (actual - forecast) for period t.

In other words, the new forecast is the old one plus an adjustment for the error that occurred in the last forecast.

Forecast for September = Forecast for August + (Actual of August - Forecast of August) x Smoothing constant

= 45 + (56 – 45) x 0.20

= 45 + 2.2

= 47.2

Forecast for October = Forecast for September + (Actual of September - Forecast of September) x Smoothing constant

= 47.2 + (63 – 47.2) x 0.20

= 47.2 + 3.16

= 50.36