DAYS TO REPAIR
The days to repair component was calculated by using the probability distribution of repair times given. This was used along with a set of random numbers based on 100 breakdowns a year. Then, a vlookup was used and the probability distribution per day to come up with the days to repair, which varies based on the random number that excel generates. The random number represents the probability of how many days it would take to repair the copier. TIME BETWEEN BREAKDOWNS

The time between breakdowns component was implemented by taking the formula for elapsed time between breakdowns as stated by Bernard Taylor III (2011). The formula is x=4√r1 where x equals the weeks between machine breakdowns and r1 equals the random number. Once the formula was entered into excel, the formula was calculated and based on the random number calculates the time between breakdowns. LOST REVENUE

The lost revenue was calculated by taking the median revenue to be earned in a given day and multiplying this by the calculated days to repair. Once this number was calculated, it was then calculated annually by taking the sum of the lost revenue column and dividing it by the cumulative time divided by 52 for 52 weeks in a year. This calculates the annual loss of revenue.

PUTTING IT ALL TOGETHER
The lost revenue for one year is $52,518.04 based on calculations in the excel spreadsheet. Confidence in this answer is very high based on research. The limits of the study are that the accurate revenue for the day was not exact so therefore an exact number cannot be determined for lost revenue. Also, the probability always stands a chance that the numbers are likely not to occur or to occur. Therefore, the numbers are not exact and could change at any time given the situation.

REFERENCES
Taylor III, Bernard W. (2011). Introduction to Management Science. Upper Saddle River, NJ: Prentice Hall

...Read the "JETCopies" 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.
There are two deliverables for this Case Problem, the Excel spreadsheet and the written description/explanation. Please submit both of them electronically via the dropbox.Assignment #1: JETCopies Case Problem
Read the "JETCopies" Case...

...JetCopies Case Study
1. 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.
2. In Excel, use a suitable method for simulating the interval between successive breakdowns, according to the continuous distribution shown.
3. In Excel, use a suitable method for simulating the lost revenue for each day the copier is out of service.
4. 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.
5. 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).
6. 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.
Answers
1.
# of days P(x) Cumulative
1 0.2 0
2 0.45 0.2
3 0.25 0.65
4 0.1 0.9
Q: 2-4.
Break Random times b/w Random Repair Random Lost cumulative
down # 1 Break (weeks) # 2 Time #3 Revenue time
1 0.78468 5.314929 0.88991 3 2237 $6,711 5.314929
2 0.512227 4.294201 0.831365 2 3244 $6,488 9.60913
3 0.389251 3.743399 0.912647 2 5874 $11,748 13.35253
4 0.998082 5.994243 0.216353 1 3330 $3,330 19.34677
5 0.963834 5.890502 0.415313 4 5487...

...JETCopies Problem
The simulation of JetCopies can be done by generating random numbers from given probability distributions. The different steps of this simulation and assumption made are explained below.
1. Simulation for the repair time.
It is given that the repair time follows
Repair Time (days) Probability
1. .20
2. .45
3. .25
4. .10
-----
1.00
To generate a random number from the above distribution, we use the following procedure.
Generate a random number denoted by r2 from between 0 and 1. If this generated random number is less than or equal to 0.2 take repair time = 1. If the generated random number is 0.2 to 0.65, we take repair time =2. If the generated random number is 0.65 to 0.90, we take repair time = 3 and take 4 otherwise.
2. Simulation for break-down Distribution
Given that the probability distributions of random variable X representing the time between break-downs varies from 0 to 6 weeks with probability increasing continuously, the copier went without breaking down can be approximated by the probability distribution
f(x) =x/18 0 < x < 6
Hence the distribution function of x is
F(x)=x2/36 0 < x < 6
If r1 is another random number generated between 0 and 1, then we can write
r1= x2/36
Hence x=6[pic]
Therefore to simulate...

...JETCopies Problem
Lost revenue of JetCopies due to breakdown can be done by generating random numbers from different probability distributions according the given probability law. The different steps of this simulation and assumption made are explained below.
1. Simulation for the repair time.
It is given that the repair time follows
|Repair Time (days) |Probability |
|1 |0.2 |
|2 |0.45 |
|3 |0.25 |
|4 |0.10 |
To generate a random number from the above distribution, we use the following procedure.
Generate a random number denoted by r2 from between 0 and 1. If this generated random number is less than or equal to 0.2 take repair time = 1. If the generated random number is 0.2 to 0.65, we take repair time =2. If the generated random number is 0.65 to 0.90, we take repair time = 3 and take 4 otherwise.
2. Simulation for break-down Distribution
Given that the probability distributions of random variable X representing the time between break-downs varies from 0 to 6 weeks with...

...Assignment #1: JETCopies Case Problem
Read the “JETCopies” 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:
1. 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.
2. In Excel, use a suitable method for simulating the interval between successive breakdowns, according to the continuous distribution shown.
3. In Excel, use a suitable method for simulating the lost revenue for each day the copier is out of service.
4. 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.
5. 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).
6. 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.
Case Problem
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...

...Running Head: JETCOPIES CASE
JETCopies Case
Math 540
Winter 2013
JETCopies Case
Introduction
Before starting the case, it is important to know how this case will be evaluated through excel, the functions and their application, and how they quantifiably accentuate on the variables and known possibilities of the case. The major functions that are used in this particular case are RANDBETWEEN and SQRT in order to identify the relationship of how they simulate and validate the confidence in the results.
RANDBETWEEN & EXCEL
Excel is an excellent application, which has many functions not only of mathematical calculations, like logic. Most people see it as a "challenge", which actually is not. Always bear in mind that Excel is nothing but a game of battleship. This is a set of lines and columns, which are the vessels, and based on the crossing of these lines and columns; seek to achieve the most likely target.
In Excel we have to view the location of each row and column, finding the respective numbers of rows and columns of letters, to achieve the desired end result. I suggest you use it to try to enter their functions, avoid the maximum use of the wizard, it somehow becomes a "settling" deprives us of better assimilate the functions. Typing functions makes it easier to memorize the commands, making the use of the tool faster and more efficient.
Run...

...JetCopies Case Problem
Shelandria Jones
Strayer University
MAT 540-Quantitative Methods
Dr. Raymond Ottinot
February 5, 2013
Introduction
JetCopies is a business venture of a couple of young men who had the insight to open up a copy business. James Ernie and Terri received a loan from Terri’s parents of $18,000. Due to information they have received the large copier they purchased has a history of breakdowns often for a few days. So the three guys are looking into possibly getting a smaller copier. The purchase of the smaller copier can be used while the other larger copier is being repaired. Before they ask anyone about loaning them any additional money they would like to come up with a simulation to show why the purchase of the smaller copier would be beneficial. The cost of the smaller copier is $12,000.
Breakdowns
I used originally 20 breakdowns but then I ended up going to 13 breakdowns. I then created a list of random numbers. The list of random numbers was figured out in excel with the formula =RAND. Which is depicted by the column r2. After obtaining these random numbers and then using the chart that was provided below I then reviewed my random numbers to see where they fell inline with the repair time day chart. The chart was gathered by Terri from the college of business in which the point was to try and get an understanding how long it would take to get the copier that...

...determine the time between breakdowns.
Weeks between Breakdowns
The time between breakdowns allows you to estimate the time between the breakdowns of the copy machine. The time between breakdown allows you to also understand how the long the copy machines will work and how long they will last before they breakdown again. In column D row 16 is where I input the formula to find the time between breakdown =6*SQRT(Random r1). I used =6*SQRT(0.862) to get the first time between breakdown in the amount of 5.570. From there I copied and pasted the formula to the remaining D column to get the rest of the time between breakdowns in weeks.
Cumulative Time
Now that the time between breakdowns is set, this will allow me to determine the cumulative time. The cumulative time allows us to determine the running time for the frequency. This is determined by adding the time between breakdowns plus the cumulative times. In column E row 16 I placed the time between breakdowns for the first random number used in D16. We then add column E to column D to get the cumulative time by copying and pasting the formula to the remaining D column E. To answer the question in the problem, the cumulative time had to equal 52 weeks (1 year) to help determine the loss of revenue.
Repair Time
The repair time determines how long it will take to repair the copy machines when they breakdown. In order to calculate the repair time we must create a new column for...