The actual demand for castings in a factory is \(500\) units and \(635\) units for the months of January 2026 and February 2026, respectively. The forecasted demand for January 2026 is \(250\) units and the smoothing constant is \(0.7\). Using the exponential smoothing method, the forecast of the demand for castings in March 2026 is ________ units (in integer).
Show Hint
Apply the exponential smoothing formula twice, first to get the February forecast, then to get March.
Step 1: Write the smoothing formula as old forecast plus a correction.
$F_{next} = F_{old} + \alpha \times \text{error}$, with error being actual minus old forecast.
Step 2: Roll the forecast forward one month at a time, since March needs February's forecast first.
January error is $500 - 250 = 250$, so February forecast is $250 + 0.7(250) = 425$.
Step 3: Roll forward again to reach March.
February error is $635 - 425 = 210$, so March forecast is $425 + 0.7(210) = 425 + 147 = 572$.
Final Answer:
Working one step at a time gives a March 2026 forecast of 572 units.
\[ \boxed{F_{Mar} = 572} \]
