A newly launched mortgage brokerage firm has established a customer service center.

Prospective homebuyers are arriving at a rate of $200$ per hour $($following a Poisson Distribution$),$

and their time spent waiting is valued at $$100$ per person per hour. The agency contracts

customer service representatives who are paid $$15$ per hour to process registrations. Each

registration session takes $1$ minute on average $($following an Exponential Distribution$),$ and there

is one queue serving multiple agents.

a$)$ Calculate the minimum number of agents required for this operation.