A powder metal (PM) manufacturing line produces bushings in three steps: compaction, sinter-harden, and rough/finish/turn, which are accomplished at three single-machine stations with average processing times of 12, 10, and 6 minutes, respectively. However, while compaction and sinter-harden are dedicated to the bushing line, the rough/finish turn station also processes bearings from another line; the average processing times for bearings are 14 minutes. Please show a diagram of the machines in their line.

a) If the production volumes of bushing and bearings are the same, what is the bottleneck of the PM line?

b) If the volume of bearings is 1/2 that of bushings, what is the bottleneck of the PM line?

c) If the volume of bearings is 1/3 that of bushings, what is the bottleneck of the PM line?

d) If you had to pick one process for the bottleneck, which one would it be?

Please show a diagram of the machines in their line.