# Assignment 1 - Quantitative Methods

**Topics:**Probability distribution, Random variable, Randomness

**Pages:**5 (1089 words)

**Published:**August 3, 2012

Assignment #1: JET Copies Case Problem

By: Jenna Kiragis

Quantitative Methods 540

7/29/2012

JET Copies Case Problempage 2

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. 1. Simulation for the repair time.

|Repair Time (days) |Probability | |1 |0.2 | |2 |0.45 | |3 |0.25 | |4 |0.1 |

The generated random number 0.2 take repair time = 1. If the generated random number is 0.2 to 0.65, the repair time will be 0.2. The random generated number of 0.65 and 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

f(x) =x/18 0 < x < 6 the distribution function of x is F(x)=x2/36 0 < x < 6between 0 and 1, then we can write r1= x2/36 In Excel, use a suitable method for simulating the lost revenue for each day the copier is out of service. To get the amount of business lost on a particular day is r3 repair time, and the lost revenue is then equal to 0.1 r3 repair time, ten cents is what they charge per copy. (Taylor 2010).

JET Copies Case Problempage 3

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 | |P (x) |Cumulative |Repair Time | |0.2 |0 |1 | |0.45 |0.2 |2 | |0.25 |0.65 |3 | |0.1 |0.9 |4 |

|Breakdown |Random |Time Between |Random |Repair |Random |Lost |Cumulative | | |r1 |Breaking (weeks) |r2 |Time |r3 |Revenue |Time | |1 |0.78468 |5.314929 |0.88991 |3 |2237 |$6,711.00 |5.314929 | |2 |0.512227 |4.294201 |0.831365 |2 |3244 |$6,488.00 |9.60913 | |3 |0.389251 |3.743399 |0.912647 |2...

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