$($Service Process Analysis$)$ Customers are going through a four$-$step process to get their product returns processed at the customer service center. Each customer will spend $3$ minutes at the check$-$in desk before going to one of two return clerks. After that, they will visit one of three inspection stations for product evaluation and then go to one of two refund stations to complete the transaction. The time spent at each step is as follows:

Check$-$in Desk: $3$ minutes

Return Clerk: $5$ minutes

Inspection Station: $15$ minutes

Refund Station: $7$ minutes

The demand rate is $40$ customers per hour.

a$.$ What is the capacity $($in customers per hour$)$ of each step?

b$.$ Which step is the bottleneck?

c$.$ What is the process capacity $($in customers per hour$)$ of the customer service center?

d$.$ What is the flow rate $($in customers per hour$)$ of the customer service center?

e$.$ Is it capacity$-$constrained or demand$-$constrained?

f$.$ What is the cycle time $($in minutes$)$ of the customer service center?

g$.$ What is the utilization of each step?