Mr$.$ Beautiful, an organization that sells weight training$$ sets, has an ordering cost of $$$$35$ for the$$ BB$-1$ set$($BB$-1$ stands for Body Beautiful Number$1).$ The carrying cost for$$ BB$-1$ is $$$$5$ per set per year. To meet$$ demand, Mr$.$ Beautiful orders large quantities of$$ BB$-14$ times a year. The stockout cost for$$ BB$-1$ is estimated to be $$$$10$ per set. Over the past several$$ years, Mr$.$ Beautiful has observed the following demand during the lead time for$$ BB$-1$:

$$

Demand During Lead Time

Probability

$40$

$0\mathrm{.}1$

$60$

$0\mathrm{.}2$

$80$

$0\mathrm{.}2$

$100$

$0\mathrm{.}2$

$120$

$0\mathrm{.}2$

$140$

$0\mathrm{.}1$

The reorder point for$$ BB$-1$ is $80$ sets. What level of safety stock should be maintained for$$ BB$-1?$

Part $2$

The optimal quantity of safety stock which minimizes expected total cost is enter your response here sets $($enter your response as a whole$$ number$).$