Floyd Distributors, Inc., provides a variety of auto parts to small local garages. Floyd purchases parts from manufacturers according to the EOQ model and then ships the parts from a regional warehouse direct to its customers. For a particular type of muffler, Floyd's EOQ analysis recommends orders with Q$*=25$ to satisfy an annual demand of $100$ mufflers. Floyd's has $250$ working days per year, and the lead time averages $15$ days.

$($a$)$ What is the reorder point if Floyd assumes a constant demand rate? $($Round your answers to the nearest integer.$)$

$($b$)$ Suppose that an analysis of Floyd's muffler demand shows that the lead$-$time demand follows a normal probability distribution with mean$=6$ and standard deviation$=2.$ If Floyd's management can tolerate one stock$-$out per year, what is the revised reorder point? $($Round your answers to the nearest integer.$)$

$($c$)$ What is the safety stock for part $($b$)?($Round your answers to the nearest integer.$)$

$($d$)$ If Ch $=$ $$4/$unit$/$year$,$ what is the extra cost $($in $ per year$)$ due to the uncertainty of demand? $($Round your answers to the nearest integer.$)$