In a batch machining operation on a conventional machine, setup time is $2\mathrm{.}5$hours and batch size is $100$units $.$ The cycle time consists of part handling time of $50$sec and processing time of $1\mathrm{.}25$min. One part is produced each cycle. Tool changes must be performed every $10$parts and this takes $3\mathrm{.}0$min. The reliability of this machine is characterized by mean time between failuers of $40$hours and a mean time to repair of $50$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 $?$