$9.[15$ points$]$ A kitchen supply store stocks a popular coffee grinder. Annual demand is $6,000$ units, the ordering cost is $\backslash (\backslash$$ $20\mathrm{.}00\backslash ),$ and the inventory holding cost is $\backslash (15\backslash \%\backslash )$ of the $\backslash (\backslash$$ $40\mathrm{.}00\backslash )$ purchase price.

a$)[5$ points$]$ What is the economic order quantity?

b$)[5$ points$]$ What is the total annual cost for this inventory item?

c$)[5$ points$]$ If the average daily demand is $24$ units with a standard deviation of $4$ units per day, and the lead time is three days, what safety stock provides a $\backslash (90\backslash \%\backslash )$ service level?