Question

Question 6.

In Question 5, suppose Monica can be replaced by another server, Jodi, who must be paid $14 per hour whereas Monica is paid $10 per hour. Jodi can serve 11 customers per hour. If a customer’s time is considered to be worth $10 per hour, is it worth to replace Monica with Jodi? Calculate the total cost of paying Monica and the customers’ time and the total cost of paying Jodi and the customers’ time to answer this question.

Reference Question 5.

Monica works at a cafeteria counter in a food court. Customers arrive at a mean rate of 7 per hour. The mean service rate is 9.5 per hour. Assume it is a single-server waiting line model.

Answer 1

Given,

Arrival rate (l) = 7 customers per hour

Service rate Monica (mm) = 9.5 customers per hour

Service Rate Jodi (md)= 11 customers per hour

Average time a customer spends in system if Monica is serving= 1/(mm-l)          

                      = 1/(9.5-7) =1/2.5 = 0.4 hour = 24 mins

Monica’s cost per customer = $10*0.4 = $4

Average time a customer spends in system if Jodi is serving= 1/(md-l)                         

= 1/(11-7) =1/4 = 0.25 hour = 15 mins

Jodi’s cost per customer = $14*0.25 = $3.5

It will be effective to hire Jodi over Monica