$($a$)$ A four$-$station line with multi$-$machine stations, where the number of parallel

machines at Stations A$,$ B$,$ C$,$ D is $2,6,10,3,$ respectively. The average machine

processing times at Stations A$,$ B$,$ C$,$ D are $10,24,40,18$ minutes, respectively. Compute

the capacity of this line $($bottleneck rate$)$ in terms of part per hour.

$($b$)$ Another four$-$station line $($single machine in each station$)$ is being designed to

replace the line in Part $($a$).$ Assume that the machine in each station has the average

processing time of $3$ minutes, but the new balanced line is expected to run under the

Practical Worst Case $($PWC$).$ What is the minimum WIP level in order to keep up with

the same throughput as the old line in Part $($a$)?$