Problem $10-31($Algorithmic$)$

A product with an annual demand of $1000$ units has $C_0=$$$35\mathrm{.}00$ and $C_h=$$$6.$ 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 $7\%$ 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.

Stock$-$out$/$cycle