A product has a reorder point of $250$ units and is ordered ten times a year. The following table shows the historical distribution of demand values observed during the reorder period.

$\backslash$table$[[$Demand$,$Probability$],[240,\mathrm{.}1],[250,\mathrm{.}2],[$rop $260,\mathrm{.}4],[270,\mathrm{.}2],[280,\mathrm{.}1]]$

Currently, stockouts are valued at $$5$ per unit per occurrence, while inventory carrying costs are $$2$ per unit per year. Should the firm add safety stock? If so$,$ how much safety stock should be added?