In a batch machining operation, setup time is $1\mathrm{.}5$ hr 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.Determine $($a$)$ average cycle time,$($b$)$ time to comptete the batch, and$($c$)$ average production rate