A company is using exponential smoothing when forecasting the demand for a product. The forecast is updated once every week.

The smoothing constant for the demand forecast is $0\mathrm{.}1,$

and for MAD a smoothing constant equal to $0\mathrm{.}2$ is used.

Last week the forecast for the demand were $250$ and MAD were $30.$

The observed demand during this week is $230.$

The supplier lead time is $3$ weeks.

Assume that forecast errors during different weeks are independent of each other.

Update the demand forecast and the forecast for MAD and then derive a forecast for the total demand during the next three weeks $($i$.$e$.,$ the lead time$)$