$4$a$.$ 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, $[2]($b$)$ cycle time, $[2]($c$)$ theoretical minimum number of workers required on the line, $[2]($d$)$ if the balance efficiency is $0\mathrm{.}93$ and the repositioning time $=6$ sec$,$ how many workers will actually be required? $[4]4$b$.$ Sketch all five automated production line configurations. $[5]$