# Question

A certain queueing system has a Poisson input, with a mean arrival rate of 4 customers per hour. The service-time distribution is exponential, with a mean of 0.2 hour. The marginal cost of providing each server is $20 per hour, where it is estimated that the cost that is incurred by having each customer idle (i.e., in the queueing system) is $120 per hour for the first customer and $180 per hour for each additional customer. Determine the number of servers that should be assigned to the system to minimize the expected total cost per hour.

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