The demand and forecast for February are $$12000$$ and $$10275,$$ respectively. Using single exponential smoothening method (smoothening coefficient $$= 0.25$$), forecast for the month of March is

A moving average system is used for forecasting weekly demand. $${F_1}\left( t \right)$$ and $${F_2}\left( t \right)$$ are sequences of forecasts with parameters $${m_1}$$ and $${m_2}$$, respectively, where $${m_1}$$ and $${m_2}\left( {{m_1} > {m_2}} \right)$$ denote the numbers of weeks over which the moving averages are taken. The actual demand shows a step increase from $${d_1}$$ to $${d_2}$$ at a certain time. Subsequently,

The sales of a product during the last four years were $$860, 880, 870$$ and $$890$$ units. The forecast for the fourth year was $$876$$ units. If the forecast for the fifth year, using simple exponential smoothing, is equal to the forecast using a three period moving average, the value of the exponential smoothing constant $$\alpha $$ is

The sale of cycles in a shop in four consecutive months are given as $$70, 68, 82 95.$$ Exponentially smoothing average method with a smoothing factor of $$0.4$$ is used in forecasting. The expected number of sales in the next month is