Mr$.$ Beautiful, an organization that sells weight training$$ sets, has an ordering cost of $$$ $40$ for the$$ BB$-1$ set$($BB$-1$ stands for Body Beautiful Number$1).$ The carrying cost for$$ BB$-1$ is $$$$18$ per set per year. To meet$$ demand, Mr$.$ Beautiful orders large quantities of$$ BB$-14$ times a year. The stockout cost for$$ BB$-1$ is estimated to be $$$$40$ per set. Over the past several$$ years, Mr$.$ Beautiful has observed the following demand during the lead time for$$ BB$-1$:

Demand During Lead Time Probability

Value $11000\mathrm{.}1$

Value $21200\mathrm{.}2$

Value $31400\mathrm{.}2$

Value $41600\mathrm{.}2$

Value $51800\mathrm{.}2$

Value $62000\mathrm{.}1$

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$).$