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MAT500 Assignment 1

# MAT500 Assignment 1 - Running head JET COPIES CASE PROBLEM...

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Running head: JET COPIES CASE PROBLEM 1 JET Copies Case Problem Strayer University MAT540 – Quantitative Methods July15, 2011

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JET COPIES CASE PROBLEM 2 JET Copies Case Problem JET Copies is a copy business opened by James, Ernie, and Terri in their duplex near a college campus. They began discussing the frequent breakdowns that may occur after borrowing the \$18,000 from Terri’s parents to buy one copier. They could either risk the breakdown and loss of revenue or buy another smaller version of the copier to handle the work while the other one was out of service. However, they wanted to first have an estimate of how much money they would be losing if they did not have a backup copier. If they lost \$12,000 or more over a year’s time, then they would purchase the smaller copier as a backup (Taylor, 2011). This paper will discuss simulation models concerning interval between breakdowns, days-to-repair, and lost revenue. All of these methods together will simulate the lost revenue due to copier breakdowns over 1 year. Interval between Breakdowns According to the continuous distribution information provided, the time between breakdowns was probably between 0 and 6 weeks. Given the probability distributions of random variable x representing the weeks between machine breakdowns varies from 0 to 6 weeks, the formula for continuous probability function for the time between breakdowns is: Taking the integral of the function yields the cumulative probability distribution function F(x) : 6 0 ; 36 2 18 1 18 ) ( 2 0 2 0 = = = x x x dx x x F x x Let F(x) = r (i.e., a random number) and solve for x .
JET COPIES CASE PROBLEM 3 To simulate the interval successive breakdowns, random numbers were generated and the result multiplied by 6 and Square root. That is, the number of weeks between machine breakdowns, x, is computed by generating random numbers for r (between 0 and one), and substituting those values into this function. Cumulative number of weeks was also generated adding the number of weeks between machine breakdowns, x, and stopping just a bit above 52 weeks for the one year simulation requirement. In Excel, the steps of this simulation are as follows. First, The “Random Number 1 (RN1)” in B15:B42 are generated using the =RAND() function in column B (or column 1). We can freeze the random numbers by first covering the cells with random numbers in them with cursor, and then copy these cells. Then, we click on “Paste Special” by using the right mouse button, and then select the “Values” option and click on “OK.” Second, to find “the time

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MAT500 Assignment 1 - Running head JET COPIES CASE PROBLEM...

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