$3\mathrm{.}4$ A flow$-$line mass production operation consists of eight manual workstations. Work units are moved synchronously and automatically between stations, with a transfer time of $15sec.$ The manual processing operations performed at the eight stations take $40sec,52sec,43sec,48sec,30sec,57sec,53sec,$ and $49sec,$ respectively. Determine $($a$)$ cycle time