You are analyzing a production line. There are five processes, labeled A through E$,$ and your widgets start at Process A$,$ then go to Process B$,$ C$,$ D$,$ and E$.$ The process map looks a bit like this:

Start $->$ A $->$ B $->$ C $->$ D $->$ E $->$ Finish.

You have the following process information:

Process A requires $10$ minutes per widget.

Process B does $4$ widgets per hour.

Process C does $4\mathrm{.}6$ widgets per hour.

Process D can do $28$ widgets per $8-$hour shift.

Process E takes $16$ minutes per widget.

What is the process time of the system? Blank $1$ minutes per widget. $($Please round to the nearest integer; if you would like to enter $12\mathrm{.}345,$ please type in a $12.)$

Which process is the bottleneck? Blank $2$

If you tied yourself to a widget just as it started Process A$,$ how many minutes later would you find yourself done with Process E$?$ Blank $3$ minutes. $($Please round to the nearest integer; if you would like to enter $12\mathrm{.}345,$ please type in a $12.$ Hint: this is another way of asking for the throughput time.$)$

Would it help make more widgets per day if we could speed up Process A by one minute per widget? Blank $4.($Please enter yes or no$).$

Say we didn't end up changing Process A after all. If we could speed Process D up by $5$ minutes per widget, what would the new process time of the system be$?$ Blank $5$ minutes. $($Please round to the nearest integer; if you would like to enter $12\mathrm{.}345,$ please type in a $12.)$

Say we did speed up Process D by those $5$ minutes per widget. Where is the bottleneck of the system now? Blank $6$