$($Prob$.1)$ Consider a three$-$step process. The first step takes $4$ minutes$/$unit$,$ the second takes $2$ minutes$/$unit$,$ and the last takes $3$ minutes$/$unit$.$ Each step requires one worker. Assume that the process has unlimited demand.

$($a$)$ What is the cycle time $($CT$)?$

$($b$)$ What is the idle time$/$unit of the process?

$($c$)$ What is the process's average utilization $($or efficiency$)?$

$($d$)$ What is the direct labor cost$/$unit if each employee gets paid $$30$ per hour?