A company uses exponential smoothing with α = ½ to forecast demand for a product. For each month, the company keeps a record of the forecast demand (made at the end of the preceding month) and the actual demand. Some of the records have been lost; the remaining data appear in the table below.

(a) Using only data in the table for March, April May, and June, determines the actual demands in April and May.
(b) Suppose now that a clerical error is discovered; the actual demand in January was 432, not 400, as shown in the table. Using only the actual demands going back to January (even though the February actual demand is unknown), give the corrected forecast for June.

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January February Mch Apr May June Forecast Actual 400 380 390 380 360 400