In a batch machining operation on a conventional machine, setup time is $1\mathrm{.}5$ hours and batch size is $80$ units. The cycle time consists of part handling time of $30$ sec and processing time of $1\mathrm{.}37$ min. One part is produced each cycle. Tool changes must be performed every $10$ parts and this takes $2\mathrm{.}0$ min. The reliability of this machine is characterized by mean time between failures of $37$ hours and a mean time to repair of $55$ min.

Determine

a$)$ Average cycle time

b$)$ Time to complete the batch

c$)$ Average hourly production rate of the machine if availability is ignored.

d$)$ Average hourly production rate of the machine if availability is taken into account.

e$)$ 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