You may need to use the appropriate technology to answer this question.

A health and nutrition store stocks a multivitamin with an annual demand of $1,000$ bottles has $C_0=$$$26\mathrm{.}50$ and $C_h=$$$7.$ The demand exhibits some variability such that the lead$-$time demand follows a normal probability distribution with $=25$ and $=5.$

$($a$)$ What is the recommended order quantity? $($Round your answer to the nearest integer.$)$

$($b$)$ What are the reorder point and safety stock if the store desires at most a $4\%$ probability of stock$-$out on any given order cycle? $($Round your answers to the nearest integer.$)$

reorder point

safety stock

$($c$)$ If a manager sets the reorder point at $30,$ what is the probability of a stock$-$out on any given order cycle? $($Round your answer to four decimal places.$)$

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