Problem $3-10($Algo$)$

The number of cases of merlot wine sold by the Connor Owen winery in an eight$-$year period is as follows:

$\backslash$table$[[,$CASES OF MERLOT$],[$YEAR$,$WINE$],[1,291],[2,377],[3,419],[4,477],[5,379],[6,521],[7,431],[8,397]]$

Using an exponential smoothing model with an alpha value of $0\mathrm{.}40,$ estimate the smoothed value calculated as of the end of year $8.$ Use the average demand for years $1$ through $3$ as your initial forecast for year $4,$ and then smooth the forecast forward to year $8.$

Note: Round your intermediate calculations and final answer to the nearest whole number.

Forecast for $8$