$9.$ 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 $200$ 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? b$.$ Suppose that an analysis of Floyd's muffler demand shows that the lead$-$time demand follows a normal probability distribution with $\backslash$mu $=12$ and $\backslash$sigma $=2\mathrm{.}5.$ If Floyd's management can tolerate one stock$-$out per year, what is the revised reorder point? c$.$ What is the safety stock for part $($b$)?$ If C$\_$h$=$$ $5/$ unit$/$year$,$ what is the extra cost due to the uncertainty of demand?