SOLUTION: Queuing Theory Suppose customers arrive at a fast-food service window at a rate of 9 people per hour. With reasonable assumptions, the average time(in hours) that a customer will

Question 1054323: Queuing Theory
Suppose customers arrive at a fast-food service window at a 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 f(x)=9/x(x-9) where x is the average # of people being served per hour.
A)Why is the function meaningless if the average # of people served per hour is less then 9?
Suppose the average time to serve a customer is 5 minutes.
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 minutes (1/8 hour). How fast must an employee work to serve a customer (on the average)?(convert to minutes)How might this reduction in serving time be accomplished?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
A) the function is negative for the average # of people served per hour is less than 9
:
B) 60 / 5 = 12 people served per hour
:
C) f(12) = 9 / (12(12-9)) = 9/36 = 1/4 = 15 minutes
:
D) 1/8 = 9 / (x(x-9))
x^2 -9x = 72
x^2 -9x -72 = 0
Use quadratic formula to solve for x
x = (9 + 19.20) / 2 = 14.10
x = (9 - 19.20) / 2 = -5.10
we want the positive value 14.10 approx 14 people
60 / 14 = 4.2857 minutes service time
Add another employee and another service window

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