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. 

b) Determine the ideal number of agents to employ. 

c) Calculate the hourly cost of operation at the ideal number of agents. 

d) Assess the utilization rate for agents with the minimum number of agents. 

e) An innovative customer experience coordinator is brought on board, offering a magician's services to entertain those waiting, at a cost of $15 per hour, thus reducing the waiting cost to $50 per person per hour. How does this affect the ideal number of agents and the associated costs?