The average rate of arrivals at a self-service store is 30 per hour. At present, the store employs a cashier who can serve an average of 45 customers per hour. Management estimates the cost of wait in the system of a customer at a rate of $10 per hour. An assistant to the cashier can be hired which would enable the cashier to serve customers an average of 75 customers per hour. If the hourly wage for the assistant is $8, would it be worthwhile hiring the assistant?

Note 1: If the assistant is hired, the new queueing system will be a “single” server model, where the cashier and assistant serve as the single server, with higher average service rate than the cashier alone.

Note 2: To perform the cost-benefit analysis of hiring an assistant you need to calculate how much the average wait time in the system is reduced by hiring an assistant and what is the corresponding reduction in average hourly “waiting cost.”