### What is the average number of customers in the waiting line

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At a small neighborhood grocery store, customers form a single line and arrive the checkout of the store at a rate of 20 per hour (Poisson). Matt, the store owner who works at the single checkout station, takes on average 2 minute (exponential) to serve a customer. Recently Matt observed that customers were very frustrated with the long wait time in the line. As a short term solution, Matt launched a promotion campaign that offers “One free 16 oz. Soda” to any customer who waits in the line more than 3 minutes. Assume that the arrival rate did not change after the campaign was launched, answer the following questions:

Part A) What is the waiting line model? What is the average number of customers in the waiting line?

Part B) If each 16 oz. soda Harry gives away costs \$1.25, what is the expected hourly cost associated with this “free soda” campaign?

Matt feels that the cost of his free soda campaign (calculated previously) is too high. He knows that if he reduces the average time spent to serve a customer, there will be less free sodas giveaway. One idea is to hire an assistant to work as a “helper” for \$10 per hour. In this case, Matt and his assistant work together as a team to check out each customer; Matt scans the grocery items and his assistant bags the groceries and puts them back in the cart. Under this approach, the average service time can be reduced to 1 minute (exponential).

Part C) If the assistant is hired, what is the waiting line model? What is the average waiting time in the line?

Part D) From the total cost point of view, would it be worthwhile hiring the assistant? If your answer is yes, explain why? If your answer is no, what is the maximum wage rate that Matt should offer the assistant?

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