A supermarket is trying to decide how many cash registers

A supermarket is trying to decide how many cash registers to keep open. Suppose an average of 18 customers arrive each hour, and the average checkout time for a customer is four minutes. Inter-arrival times and service times are exponentially distributed, and the system can be modeled as an M/M/s system. (In contrast to the situation at most supermarkets, we assume that all customers wait in a single-line.) It costs $20 per hour to operate a cash register, and a cost of $0.25 is assessed for each minute the customer spends in the cash register area (in line or being served). How many registers should the store open to minimize the expected hourly cost?

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