Problem $10-31($Algorithmic$)$

A product with an annual demand of $900$ units has $C_O=$$$18\mathrm{.}00$ and $C_h=$$$7.$ The demand exhibits some variability such that the lead$-$time demand follows a

normal probability distribution with $=24$ and $=4.$

Note: Use Appendix B to identify the areas for the standard normal distribution.

a$.$ What is the recommended order quantity? Round your answer to the nearest whole number.

$Q^{**}=$

b$.$ What are the reorder point and safety stock if the firm desires at most a $4\%$ probability of stock$-$out on any given order cycle? If required, round your

answers to the nearest whole number.

Record point $=$

Safety stock $=$

c$.$ If a manager sets the reorder point at $29,$ what is the probability of a stock$-$out on any given order cycle? If required, round your answer to four decimal

places. Round $z$ value to two decimals.

$P($ Stock$-ou\frac{t}{c}$ycle $)=$

How many times would you expect a stock$-$out during the year if this reorder point were used? Round your answer to the nearest whole number.

Number of Stock$-$outs$/$year $=$