A company is using exponential smoothing when forecasting the demand for a special 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 and MAD were $250$ and $30,$ respectively. 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.

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 this special product 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 $95\%.$