One is to use exponential smoothing when forecasting the demand for a product.

The forecast is updated once every week.

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

The smoothing constant for MAD is $0\mathrm{.}2$

Last week the forecast demand was $250$

Last week the MAD was $30$

The observed demand during this week is $230.$

The lead time is $3$ weeks.

Forecast errors during different weeks are independent of each other.

With the above information we get that

$-$ The updated demand forcast for newt week I $248$ units.

$-$ The updated forcast for MAD is $28$

$-$ and the forecast for the total demand during the next $3$ weeks are $744$

Assume that the inventory for theproduct is controlled by an $($R$,$Q$)$ policy with continuous review. Assume that Q$=120$ and that the demand during the lead time follows a normal distribution. Determine the lowest value of safety stock, SS$,$ such that both S$\_1$ and S$\_2$ are at least $95\%.$