The local driver's license center processes applications for driver's license renewals through the following three steps. First, the customer registers with the receptionist, who updates the customer's information in the database. This first step takes $4$ minutes per customer. Then, the customer visits one of $3$ cashiers to pay the associated fees for the license renewal. This takes $9$ minutes per customer because several forms must be printed from the computer and signed by the customer. Finally, the customer visits one of $3$ license processing stations where the customer's picture is taken and the license is printed. This final step takes $15$ minutes per customer.

a$.$ Assuming unlimited demand, what is the flow rate of the process in customers per hour? $($Round to nearest integer.$)$

b$.$ If demand is $7$ customers per hour, what is the utilization of the receptionist?

$($Round to nearest integer.$)$ percent

c$.$ If demand is $7$ customers per hour, what is the cycle time $($minutes$)$ of the process? per hour $($Round your answer to $2$ decimal places.$)$ minutes

d$.$ If the system starts empty and operates worker paced, how long does it take to complete the processing of $9$ customers?

$($Round your answer to $2$ decimal places.$)$

e$.$ Assuming unlimited demand, what would the new flow rate be if the center added one server to the bottleneck resource?

$($Round your answer to $2$ decimal places.$)$