Average demand for a shave lotion in a fragrance store is $10$ units per day and standard deviation

of demand is $2$ units per day which distributes normally.

The salesperson of shave lotion producer arrives at the fragrance store once in $10$ days, controls the

inventory and gives orders to his company in amount of the difference between maximum inventory

and on$-$hand inventory. The order given arrives in $2$ days and the fragrance store wishes $95$ percent

cycle service level. $($z$=1,65)$

a$)$ Find out maximum inventory?

b$)$ The salesperson in his arrive counts $30$ numbers of shave lotions in shelf. So$,$ how many shave lotions

should he order to his company?