Q$.2$ A batch manufacturing operation has a machine setup time of $5\mathrm{.}0$ hours and a manufacturing time of $1\mathrm{.}70$ min per cycle. Six components are produced each cycle. Part handling time each cycle is $40$ sec $.$ Tool changes must be performed every $10$ parts and this takes $3\mathrm{.}0$ min $.$ It consists of the worker obtaining six starting work units from a parts tray, loading them into the machine, and then after processing, unloading the completed units and placing them into the same tray. Each tray holds $30$ work units. When all of the starting work units have been replaced with completed units, the tray of completed parts is moved aside and a new tray of starting parts is moved into position at the machine. This irregular work element takes $5\mathrm{.}0$ min $.$ Batch quantity is $2700$ units. Determine

$[6]$

i$.$ Average cycle time

ii$.$ Time to complete the batch

iii. Average production rate.