George G, Teacher at Home Tutor Hotline, Numerade Educator

00:14

Calculus 3

A fast-food franchise is considering operating a drive-up window
food-service operation. Assume that customer arrivals follow a
Poisson probability distribution, with an arrival rate of 24 cars
per hour, and that service times follow an exponential probability
distribution. Arriving customers place orders at an intercom
station at the back of the parking lot and then drive to the
service window to pay for and receive their orders. The following
three service alternatives are being considered:
System A: A single-server operation in which one employee fills
the order and takes the money from the customer. The average
service time for this alternative is 2 minutes.
System B: A single-server operation in which one employee fills
the order while a second employee takes the money from the
customer. The average service time for this alternative is 1.25
minutes.
System C: A two-server operation with two service windows and
two employees. The employee stationed at each window fills the
order and takes the money for customers arriving at the window. The
average service time for this alternative is 2 minutes for each
server.
The following cost information is available.
Customer waiting time is valued at $25 per hour to reflect the
fact that waiting time is costly to the fast-food business.
The cost of each employee is $6.50 per hour.
To account for equipment and space, an additional cost of $20
per hour is attributable to each server.
What is the lowest-cost design for the fast-food business? If
required, round your answers to two decimal
places.
Total Cost
System A
$
System B
$
System C
$
System A, B or
C is the most economical?