$2)$ 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.