Consider a $3-$stage serial process in which the product has to be processed at Stage A$,$ Stage B$,$ and then Stage C$.$ The processing times at Stage A$,$ Stage B$,$ and Stage C are $12$ min$/$unit$,8$ min$/$unit$,$ and $10$ min$/$unit$,$ respectively. Different stages are performed by different resources, and there is no variability in processing times.

$($a$)$ What is the minimum cycle time of the process?

min$/$unit

$($b$)$ What is the maximum throughput rate of the process?

units$/$hour

$($c$)$ What is the minimum throughput time of the process?

minutes