Consider a fast initial car inspection process with the following steps:

$$ Initial check$-$in: this step is done by $4$ clerks with identical training and average service time of $10$

minutes.

$$ External examination: there are $8$ specialists and the average examination takes $20$ minutes. Per

patient.

$$ Mechanical examination: conducted by $12$ mechanics and on average it takes $30$ minutes.

$1.$ What is the bottleneck rate, the raw process time, and the critical WIP?

$2.$ 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