Example $3$

A single model assembly line is being planned to produce a consumer appliance at the rate of $200,000$ units per year. The line will be operated $8$ hours per shift, two shifts per day, five days per week, $50$ weeks per year. Work content time $=35\mathrm{.}0$min. For planning purposes, it is anticipated that the proportion uptime on the line will be $95\%.$ Determine $($a$)$ average hourly production rate, $($b$)$ cycle time, and $($c$)$ theoretical minimum number of workers required on the line. $($d$)$ If the balance efficiency is $0\mathrm{.}93$ and the repositioning time $=6$ sec$,$ how many workers will actually be required?