In a batch machining operation on a conventional machine, setup time is $15$ hours and batch size Is $80$ units. The cyde hime 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 $20$ min. The reliability of this machine is charactenzed by mean time between failures of $37$ hours and a mean time to repair of $55$ min. Determine

a$)$ Average oycle time

b$)$ Time to comptere the batch

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

d$)$ Average hourty production rate of the machine il avalabity is laken into account

e$)$ Suppose that availability only applied dunng the actual run time of the machine and not the setup lime Determane the average hourly production rate of the machine.