QUESTION $4$

Etsy$$s & Company orders a particular type of Christmas decoration once a year. The

purchasing price is $$6$ per unit. It costs $$2$ to hold one unit in stock and there is a shortage cost

of $$10$ per unit. The demand density function is given by

$()=$ &

$1$

$100),0<=<=100$

$0,$

Find the optimal order quantity if the amount on hand before an order is placed is $($i$)25$ units,

$($ii$)50$ units.