$(5$ points$)$ A machine$-$paced production facility has six stations with processing times of $30,20,25,28,22,$ and $24$ seconds per unit, respectively. The process is capacity$-$constrained and runs on a $30-$second$/$unit cycle time.

$($a$)$ What is the total idle time across all six stations?

$($b$)$ What is the average labor utilization?