$3\mathrm{.}5$ Average setup time on a certain production machine is $6\mathrm{.}0$ hr$.$ Average batch size is $40$

parts, and average operation cycle time is $2\mathrm{.}5$ min. The reliability of this machine is characterized

by mean time between failures of $40$ hr and a mean time to repair of $35$ min.

$($a$)$ If availability is ignored, what is the average hourly production rate of the machine?

$($b$)$ Taking into account the availability of the machine, determine its average hourly production

rate. $($c$)$ Suppose that availability only applied during the actual run time of the

machine and not the setup time. Determine the average hourly production rate of the machine

under this scenario