A fastener production unit has a bolt manufacturing cell. The cell has three workstations, a milling station, a drilling station, and a packing station. The milling station has five parallel millers, with a natural capacity of $20$ parts$/$hour each. The drilling station has three parallel drills, with a natural capacity of $30$ parts$/$hour each. The packing station has a single manual packer with a natural capacity of $80$ parts$/$hour$.$

The milling station is maintained every $750$ hours and the maintenance lasts $250$ hours. The drilling station is maintained every $891$ hours and the maintenance lasts $99$ hours. The packer is never down during a shift and is therefore available all the time. Note: the availability calculated may be assumed to apply to the entire station and no need to apply them to each machine individually.

What is the critical work$-$in$-$process in this manufacturing cell?

If $70$ bolts have to be completed each hour, arrivals following an exponential distribution, and the squared coefficient of variation of process times for the milling, drilling, and packing stations are $1\mathrm{.}15,1\mathrm{.}25,$ and $0\mathrm{.}95,$ respectively:

Calculate the total time it takes for a bolt to be completed.

Calculate work$-$in$-$process in the manufacturing cell.

Is the WIP calculated in part B different from the critical WIP calculated in question $1?$ Explain the reason for the difference.