Litely Corp sells $1,350$ of its special decorator light switch per year,

and places orders for $300$ of these switches at a time.

Assuming no safety stocks, Litely estimates a $50\%$ chance of no

shortages in each cycle, and the probability of shortages of $5,10,$

and $15$ units as $0\mathrm{.}2,0\mathrm{.}15,$ and $0\mathrm{.}15$ respectively.

The carrying cost per unit per year is calculated as $$5$ and the

stockout cost is estimated at $$6($$$3$ lost profit per switch and

another $$3$ lost in goodwill, or future sales loss$).$

What level of safety stock should Litely use for this product?

$($Consider safety stock of $0,5,10,$ and $15$ units