SHOW FULL WORK/EQUATIONS: A residential construction company has opened a registration office. Customers arrive at the rate of 200 per hour (Poisson Distribution) and the cost of their waiting in the queue is estimated $100 per person per hour. The local convention bureau provides servers to register customers at the fee of $15 per person per hour. Registration process takes 1 minute (Exponential Distribution) and a single waiting line, with multiple servers is set up. a) Compute the minimum number of servers for this system (3 marks). b) Compute the optimal number of servers for this system (8 marks). c) What is the cost of system (per hour) at the optimum number of servers? (2 marks) d) Compute the server utilization rate with the minimum number of servers. (3 marks) e) A new registration manager is hired who initiates a program to entertain the people in line with juggler whom she pays $15/hour. This reduces the waiting cost to $50/hour. What is the optimal number of servers and the cost of that in this case? (9 marks)

If you include a table, please explain how you obtained each value.