Consider the following batch flow process consisting of three process steps each performed by a dedicated machine with the following information.

Step $1$: Machine $1($batch size$=5$ jobs; Set$-$up time$=10$ min$/$batch; Processing time per job$=6$ min$)$

Step $2$: Machine $2($batch size$=5$ jobs; Set$-$up time$=20$ min$/$batch; Processing time per job$=12$ min$)$

Step $3$: Machine $3($batch size$=5$ jobs; Set$-$up time$=30$ min$/$batch; Processing time per job$=8$ min$)$

Work is processed in batches at each step. Before a batch is processed at each step, the machine has to be set up$.$ During a setup, the machine is unable to process any product. Assuming that the system starts empty, what is the total completion time of an order of $20$ jobs?