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Math 540

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JET Copies Case Problem page 1

Assignment #1: JET Copies Case Problem

By: Jenna Kiragis

Quantitative Methods 540

7/29/2012

JET Copies Case Problem page 2

Case Problem

JET Copies is a copy business opened by James, Ernie, and Terri, three students who wanted to make it more convenient for other students in their apartment complex to get copies in a timely manner. After obtaining a copy machine for the business with a loan from Terri’s mother, the students soon began discussing the frequent breakdowns that may occur. It was then that the three decided they needed a backup copier. However, the students wanted to first have an estimate of how much money they would be losing if they did not have a backup copier (Taylor, 2010). This paper will discuss methods that simulate the number of days needed to repair the copier, the intervals between successive breakdowns, and the lost revenue for each day the copier is out of service. All of these methods together will simulate the lost revenue due to copier breakdowns over 1 year.

JET Copies Case Problem page 3
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.
Lost revenue of Jet Copies 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 |0.1 |

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

JET Copies Case Problem page 4
Hence x=6[pic]
Therefore to simulate from the break down distribution, generate a random number r1 between 0 and 1 and make the transformation, x=6[pic].
In Excel, use a suitable method for simulating the lost revenue for each day the copier is out of service.
3. Simulation for Lost Revenue.
It is given that the number of copies sold per day follows a uniform probability distribution between 2,000 and 8,000 copies. The revenue loss random number per day can be obtained by generating a uniform random number r3 between 2000 and 8000. Since the number of copies sold per day is a uniform probability distribution between 2000 to 8000 copies, r3 is a random number between 2000 and 8000. To get the amount of business lost on a particular day is r3 repair time, and the lost revenue is then equal to0.1 r3 repair time, since they charge $0.10 per copy.
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.
1. Repair Distribution
Px }

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