Question $3,$ Problem

HW Score: $37\mathrm{.}5\%,1\mathrm{.}5$ of

$12\mathrm{.}45$

$4$ points

$\backslash$times $)$ Points: $0$ of $1$

Mr$.$ Beautiful, an organization that sells weight training sets, has an ordering cost of $$45$ for the BB$-1$ set $($BB$-1$ stands for Body Beautiful Number $1).$ The carrying cost for BB$-1$ is $$10$ per set per year. To meet demand, Mr$.$ Beautiful orders large quantities of BB$-17$ times a year. The stockout cost for BB$-1$ is estimated to be $$15$ per set. Over the past several years, Mr$.$ Beautiful has observed the following demand during the lead time for BB$-1$:

$\backslash$table$[[$Demand During Lead Time,Probability$],[10,0\mathrm{.}1],[30,0\mathrm{.}2],[50,0\mathrm{.}2],[70,0\mathrm{.}2],[90,0\mathrm{.}2],[110,0\mathrm{.}1]]$

The reorder point for BB$-1$ is $50$ sets. What level of safety stock should be maintained for BB$-1?$

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