Jet copies | Mathematics homework help

Read the “JET Copies” Case Problem on pages 678-679 of the text. Using simulation estimate the loss of revenue due to copier breakdown for one year, as follows:

In Excel, use a suitable method for generating the number of days needed to repair the copier, when it is out of service, according to the discrete distribution shown. 

In Excel, use a suitable method for simulating the interval between successive breakdowns, according to the continuous distribution shown. 

In Excel, use a suitable method for simulating the lost revenue for each day the copier is out of service. 

Put all of this together to simulate the lost revenue due to copier breakdowns over 1 year to answer the question asked in the case study. 

In a word processing program, write a brief description/explanation of how you implemented each component of the model. Write 1-2 paragraphs for each component of the model (days-to-repair; interval between breakdowns; lost revenue; putting it together). 

Answer the question posed in the case study. How confident are you that this answer is a good one? What are the limits of the study? Write at least one paragraph. 

JET Copies 

James Banks was standing in line next to Robin Cole at Klecko’s 

Copy Center, waiting to use one of the copy machines. “Gee, 

Robin,I hate this,”he said.“We have to drive all the way over here 

from Southgate and then wait in line to use these copy machines. 

I hate wasting time like this.” 

“I know what you mean,”said Robin.“And look who’s here.A 

lot ofthese students are from Southgate Apartments or one ofthe 

other apartments near us. It seems as though it would be more 

logical ifKlecko’s would move its operation over to us,instead of 

all ofus coming over here.” Case Problems 679 

James looked around and noticed what Robin was talking 

about. Robin and he were students at State University, and most 

of the customers at Klecko’s were also students. As Robin 

suggested, a lot of the people waiting were State students who 

lived at Southgate Apartments,where James also lived with Ernie 

Moore.This gave James an idea,which he shared with Ernie and 

their friend Terri Jones when he got home later that evening. 

“Look,you guys,I’ve got an idea to make some money,”James 

started. “Let’s open a copy business! All we have to do is buy a 

copier, put it in Terri’s duplex next door, and sell copies. I know 

we can get customers because I’ve just seen them all at Klecko’s. 

Ifwe provide a copy service right here in the Southgate complex, 

we’ll make a killing.” 

Terri and Ernie liked the idea, so the three decided to go into 

the copying business. They would call it JET Copies, named for 

James, Ernie, and Terri. Their first step was to purchase a copier. 

They bought one like the one used in the college ofbusiness office 

at State for $18,000. (Terri’s parents provided a loan.) The com- 

pany that sold them the copier touted the copier’s reliability, but 

after they bought it,Ernie talked with someone in the dean’s office 

at State,who told him that the University’s copier broke down fre- 

quently and when it did,it often took between 1 and 4days to get 

it repaired.When Ernie told this to Terri and James,they became 

worried. If the copier broke down frequently and was not in use 

for long periods while they waited for a repair person to come fix 

it, they could lose a lot of revenue. As a result, James, Ernie, and 

Terri thought they might need to purchase a smaller backup 

copier for $8,000 to use when the main copier broke down. 

However,before they approached Terri’s parents for another loan, 

they wanted to have an estimate of just how much money they 

might lose if they did not have a backup copier. To get this esti- 

mate, they decided to develop a simulation model because they 

were studying simulation in one oftheir classes atState. 

To develop a simulation model,they first needed to know how 

frequently the copier might break down—specifically, the time 

between breakdowns. No one could provide them with an exact 

probability distribution,but from talking to staffmembers in the 

college ofbusiness,James estimated that the time between break- 

downs was probably between 0 and 6 weeks,with the probability 

increasing the longer the copier went without breaking down. 

Thus,the probability distribution ofbreakdowns generally looked 

like the following: 

Next, they needed to know how long it would take to get the 

copier repaired when it broke down. They had a service contract 

with the dealer that “guaranteed”prompt repair service. However, 

Terri gathered some data from the college of business from which 

she developed the following probability distribution ofrepair times: 

Repair Time (days) Probability 

1 .20 

2 .45 

3 .25 

4 .10 

1 .00 

Finally, they needed to estimate how much business they would 

lose while the copier was waiting for repair. The three of them had 

only a vague idea of how much business they would do but finally 

estimated that they would sell between 2,000 and 8,000 copies per day 

at $0.10 per copy. However, they had no idea about what kind of 

probability distribution to use for this range ofvalues.Therefore,they 

decided to use a uniform probability distribution between 2,000 and 

8,000 copies to estimate the number ofcopies they would sell per day. 

James,Ernie,and Terri decided that iftheir loss ofrevenue due to 

machine downtime during 1 year was $12,000 or more, they should 

purchase a backup copier. Thus, they needed to simulate the break- 

down and repair process for a number of years to obtain an average 

annual loss ofrevenue.However,before programming the simulation 

model,they decided to conduct a manual simulation ofthis process for 

1 year to see ifthe model was working correctly.Perform this manual 

simulation for JET Copies and determine the loss ofrevenue for 1 year. 

(Bernard W. Taylor. Introduction to Management Science, 10th Edition. Prentice Hall/CourseSmart, 02/23/2009. 678 – 679). 

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