Queuing theory (also known as waiting-line theory) investigates the problem of providing adequate service economically to customers waiting in line. Suppose customers arrive at a fast-food service window at the rate of 9 people per hour. With reasonable assumptions, the average time (in hours) that a customer will wait in line before being served is modeled by

where x is the average number of people served per hour. A graph of ƒ(x) for x > 9 is shown in the figure.

(a) Why is the function meaningless if the average number of people served per hour is less than 9?

Suppose the average time to serve a customer is 5 min.

(b) How many customers can be served in an hour?

(c) How many minutes will a customer have to wait in line (on the average)?

(d) Suppose we want to halve the average waiting time to 7.5 min A1 8 hr B. How fast must an employee work to serve a customer (on the average)?

Transcribed Image Text:

9. f(x) = x(x – 9)