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

$$

Demand During Lead Time

$100120140160180200$

Probability

$0\mathrm{.}10\mathrm{.}20\mathrm{.}20\mathrm{.}20\mathrm{.}20\mathrm{.}1$

The reorder point for$$ BB$-1$ is $140$ sets. What level of safety stock should be maintained for$$ 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$).$