Please answer ALL in EXCEL Queuing Theory Directions: Answer the following questions and submit as an Excel spreadsheet

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Please answer ALL in EXCEL Queuing Theory Directions: Answer the
following questions and submit as an Excel spreadsheet with
calculations for full credit. Excel QM is a fine tool to complete
most of these problems. In addition, it is expected that the
answers to these problems will be presented in a professional and
masters level manner.
Problem #1 The Green furniture store
gets an average of 45 customers per shift. The manager of
Greens wants to calculate whether he should hire 1, 2, 3, or 4
salespeople. He has determined that average waiting time will
be 8 minutes with 1 salesperson, 4 minutes with 2 sales people, 3
minutes with 3 salespeople and 2 minutes with 4 salespeople.
He has estimated the cost per minutes with customers wait at
$1. The cost per salesperson per shift (including benefits)
is $75.
How many salespeople should be hired? Please show your
work.
Problem #2 The Rockwell Electronics
Corporation retains a service crew to repair machine breakdowns
that occur on an average of 3 per day (approximately Poisson in
nature).
The crew can service an average of 8 machines per day, with a
repair time distribution that resembles the exponential
distribution.
(a) What is the utilization rate of this service
system?
(b) What is the average downtime for a machine that is
broken?
(c) How many machines are waiting to be serviced at any
given time?
(d) What is the probability that more than one machine is
in the system?
Problem #3 From historical data,
Harry’s Car Wash estimates that dirty cars arrive at the rate of 9
per hour all day Saturday. With a crew working the wash line, Harry
figures that cars can be cleaned at the rate of one every 5
minutes. One car at a time is cleaned in this example of a
single-channel waiting line.
Assuming Poisson arrivals and exponential service times, find
the
(a) average number of cars in line.
(b) average time a car waits before it is washed.
(c) average time a car spends in the service system.
(d) utilization rate of the car wash.
Problem #4 Mike Dreskin manages a
large Los Angeles movie theater complex
called Cinema I, II, III, and
IV. Each of the four auditoriums plays a different film; the
schedule is set so that starting times are staggered to avoid the
large crowds that would occur if all four movies
started at the same time. The theater has a single ticket booth and
a cashier who can maintain an average service rate of 270 movie
patrons per hour. Service times are assumed to follow an
exponential distribution. Arrivals on a typically active day are
Poisson distributed and average 205 per hour.
To determine the efficiency of the current ticket operation,
Mike wishes to examine several queue operating characteristics.
(a) Find the average number of moviegoers waiting in line
to purchase a ticket.
(b) What percentage of the time is the cashier busy?
(c) What is the average time that a customer spends in the
system?
(d) What is the average time spent waiting in line to get
to the ticket window?
(e) What is the probability that there are more than two
people in the system?
Problem #5 A university cafeteria
line in the student center is a self-serve facility in which
students select the food items they want and then form a
single line to pay the cashier. Students arrive at the cashier at a
rate of about four per minute according to a Poisson distribution.
The single cashier ringing up sales takes about 12 seconds per
customer, following an exponential distribution.
(a) What is the probability that there are more than two
students in the system?
(b) What is the probability that the system is empty?
(c) How long will the average student have to wait before
reaching the cashier?
(d) What is the expected number of students in the
queue?