$6\mathrm{.}17($A$)$ A part is to be produced on an automated production line. Total work content time to make

the part is $36$ min, and this work will be divided evenly among the workstations, so that the processing

time at each station is $36/$n$,$ where number of stations. In addition, the time required to transfer parts

between workstations is $6$ sec$.$ Thus, the $.$ In addition, it is anticipated that the station breakdown

frequency will be $0\mathrm{.}005,$ and that the average downtime per breakdown will be $8\mathrm{.}0$ min. $($a$)$ How many

workstations should be included in the line to maximize production rate? Also, what are $($b$)$ the hourly

production rate and $($c$)$ line efficiency for this number of stations?