mework

Question $10,$ Problem $12\mathrm{.}44$

HW Score: $35\mathrm{.}9\%,4\mathrm{.}67$ of $13$ points

Points: $0$ of $1$

Tobacco is shipped from North Carolina to a cigarette manufacturer in Cambodia once a year. The reorder point, without safety stock, is $200$ kilos. The carrying cost is $$10$ per kilo per year, and the cost of a stockout is $$75$ per kilo per year. Given the following demand probabilities during the lead time, how much safety stock should be carried?

$\backslash$table$[[$Demand During Lead Time $($Kilos$),$Probability$],[0,0\mathrm{.}1],[100,0\mathrm{.}1],[200,0\mathrm{.}2],[300,0\mathrm{.}4],[400,0\mathrm{.}2]]$

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