A $12-$station automated production line operates with an ideal cycle time of $0\mathrm{.}72$ min. Breakdowns

occur at a rate of once every $45$ cycles on average, and the average downtime per breakdown is $7\mathrm{.}8$ min.

The production line is located in a plant that works an $8-$hr day, $5$ days$/$wk$.$ Determine $($a$)$ line efficiency

and $($b$)$ number of parts the production line produces in a $40-$hr week