A lean system has $23$ containers, each of which can hold $10$ parts. The lead time required to round$-$trip one container through the system is four hours. The required safety stock is $15$ percent.

a$.$ What is the maximum demand rate this system can accommodate? Do not round intermediate calculations, Round your answer to the nearest whole number. parts$/$hr

b$.$ The company wants to accommodate double the maximum demand rate found in $($a$).$ What are all the ways the system could be changed to accomplish this?

I. Reduce $S$ to $7\mathrm{.}5\%$

II$.$ Double # of containers

III. Reduce $T$ to $2hr.$

IV$.$ Increase $C$ to $20$ parts