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A health and nutrition store stocks a multivitamin with an annual demand of $1,000$ bottles has

Co $=$ $$23\mathrm{.}50$

and

Ch $=$ $$9.$

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.$)$

$72$

$72$

$($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$34$

$34$

safety stock$9$

$9$

$($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.$)$

$0\mathrm{.}1587$

$0\mathrm{.}1587$

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.$)$

$2$

$2$