Problem $2$: Car Check Unbalanced Process

Consider the system from the last problem with the following stations:

$$ Station $1$ has $4$ identical clerks with average service time of $15$ minutes per car.

$$ Station $2$ has $8$ identical inspectors with average process time of $25$ minutes per car.

$$ Station $3$ has $12$ mechanics with average mechanical inspection time of $30$ minutes per car.

$1.$ What are the bottleneck rate rb$,$ the raw process time T$0,$ and the critical WIP w$0?$

$2.$ Compute the average cycle time when the WIP level is set at $20$ cars, under the assumptions of:

a$.$ Best case

b$.$ Worst case

c$.$ Practical worst case