What is the optimal order quantity for $Q\mathrm{.}12($purchase cost $=$$$15,$ selling price $=$$$25,$ and salvage value $=$$$10),$ given the following table of $($regular$)$ demand distribution $($e$.$g$.,20\%$ of chance the demand is $1$ unit, $10\%$ of chance the demand is $2$ units, etc.$)?$

Demand Quantity

Probability

$0\mathrm{.}2$

$1$

$q,$

$q,$

$q,($i$)$

W$)$

m

$q,2$

$($y$)$

$($i$)$

$($

$2$

$0\mathrm{.}1$

$3$

$0\mathrm{.}1$

$4$

$0\mathrm{.}2$

$5$

$0\mathrm{.}3$

$6$

$0\mathrm{.}1$

$4$

$3$

$5$

$6$