Suppose that an HMO system for processing pre$-$natal care and baby delivery insurance claims involves

three primary steps $($which we will call steps A$,$ B$,$ and C$)$ in a sequential manner. Employees work in

parallel on separate claims at each step.

The following table shows the number of employees working on each step, and the processing time per

claim per employee.

Step # of Employees Time Required$/$Claim$/$Employee

A $4010$ minutes

B $104$ minutes

C $306$ minutes

$($a$)$ Find the raw process time $($meaning the total processing time, ignoring any waiting time$)$ for an

insurance claim.

$($b$)$ Find the capacity of each step and identify the bottleneck step. What is the capacity of the system?

$($c$)$ If all steps are working at exactly the bottleneck rate, and the time in system for all claims is equal to

the raw process time, how many claims, on average, are in the system?