8. Jim McDonald, manager of the fast-food hamburger restaurant McBurger, realizes that providing fast service isa key to the success of the restaurant. Customers who have to wait very long are likely to go to one of the otherfast-food restaurants in town next time. He estimates that each minute a customer has to wait in line beforecompleting service costs him an average of 30 cents in lost future business. Therefore, he wants to be sure thatenough cash registers always are open to keep waiting to a minimum. Each cash register is operated by a part-time employee who obtains the food ordered by each customer and collects the payment. The total cost foreach such employee is $9 per hour.During lunch time, customers arrive according to a Poisson process at a mean rate of 66 per hour. The timeneeded to serve a customer is estimated to have an exponential distribution with a mean of 2 minutes.Determine how many cash registers Jim should have open during lunch time to minimize his expected total costper hour.

Given- Arrival rate (λ) = 66 per hourService rate (μ) = 602=30 per hour

Answered: 8. Jim McDonald, manager of the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.4: Important Queueing Relationships

Problem 6P

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