A product whose work content time $=60\mathrm{.}0$ min is to be assembled on a manual production line. Required production rate is $30$ units$/$hr$.$ From previous experience, it is estimated that proportion uptime $=0\mathrm{.}91,$ balance efficiency $=93\%,$ and repositioning time $=6$ sec$.$ Determine $($a$)$ the cycle time, and $($b$)$ the ideal minimum number of workers required on the line