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:

YEAR CASES OF MERLOT WINE

$1272$

$2358$

$3400$

$4458$

$5360$

$6502$

$7412$

$8378$

Using an exponential smoothing model with an alpha value of $0\mathrm{.}20,$ 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.