Response to the following problem:
Between the hours of 1 P.M. and 5 P.M. customers arrive at the downtown New York ticket office of United Airlines at the rate of 50 per hour. The average time a ticket agent spends with a customer is 6 minutes. Ticket agents earn $ 20 per hour in wages and benefits, and United Airlines estimates the goodwill cost of a customer waiting to begin service is $25 per hour while the goodwill cost of a customer being served is $5 per hour.
Assuming customers arrive according to a Poisson distribution and service time follows an exponential distribution, determine the optimal number of ticket agents that United Airlines should have working in the New York ticket office between 1 P.M. and 5 P.M.