Problem:
During lunch hours, customers arrive at a bank according to a Poisson process. The average time between two consecutive arrivals is 1 minute, and each teller can process, on average, 20 customers per hour. Assume that arrival follows Poisson distribution and the service time follows exponential distribution. Also to ally customer complaints about long wait, the bank has the following marketing slogan: "If your wait in the queue exceeds 3 minutes, you will receive $5". Assuming that each teller costs $30 per hour, determine the minimum total cost that this bank will incur. What is the number of servers that can achieve this cost?