Assignment:
Consider a cashier at a grocery store. Customers arrive at this cashier’s station according to a Poisson process with a mean of 25 customers/h. The cashier’s service times are exponentially distributed with a mean of 2 min. By hiring a person to help the cashier bagging the groceries and occasionally assist customers by bringing their groceries to their car, the mean service time for the checkout station can be reduced to 1 min. The service times are still exponentially distributed. Hiring a cashier’s aid would incur a cost of $10 per hour for the store. Furthermore, it has been estimated that the store is facing a waiting cost (lost profit and future lost sales) of $0.10 per minute that a customer spends in line or in the checkout station. The store manager wants to determine whether proceeding to hire a cashier’s aid is a good idea or not. The criterion is that the manager wants to minimize the expected total costs. What is your recommendation after analyzing the situation using an appropriate queuing model?
Provide complete and step by step solution for the question and show calculations and use formulas.