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## MAT 540 QuantitativeMethodsWeek3

by: Experthelper Notetaker

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# MAT 540 QuantitativeMethodsWeek3

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MAT 540 QuantitativeMethodsWeek3
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Date Created: 11/09/15
MAT 540  Quantitative Methods  Week 3 – Assignment #1 JET Copies Case Problem Days to Repair In determining the average repair time for the copier, I used the discrete probability distribution  given.  From that distribution, I developed a simulation model for 100 repairs.  Using computer  generated random numbers and the vertical lookup method, a simulation of the number of days  that it would take to complete each repair was developed.  From this simulation, it was  determined that the average number of days that it would take to repair the copier is 2.29 days. Interval Between Breakdowns Next, I needed to determine the interval between breakdowns (weeks).  To begin, I took the  information from the “days to repair” component and implemented it into the second component, to find the average interval between breakdowns.  Again, I used a sample of 100 breakdowns and computer generated random numbers.  From the information given in the case study that the time between breakdowns was between 0 and 6 weeks, I used the formula (x = 6√r ) for a continuous  1 probability distribution to find the number of weeks.  From the use of this formula, it was  determined that the average time between breakdowns is 3.88 weeks. Lost Revenue In my simulation model to determine the amount of revenue loss in 1 year due to copier  breakdowns and repair times, I took the average time between breakdowns (3.88 weeks),  determined that in a given year approximately 14 breakdowns would occur and calculated the  demands for 4 days.  To determine the demand for the 4 days per breakdown, I used the formula  given us (Z=6r+2).  I used the formula and random numbers for each of the 4 days to calculate  the demand of copies for each day.  In the copies lost column, I took the average of the 4 days.   To find the amount of revenue that would be lost due to breakdowns and repair times, I  multiplied the daily average copies lost amount by 1000, then multiplied by \$0.10 per copy  revenue.  The revenue lost for 14 breakdowns (occurring approximately every 4 weeks within 1  year) totaled \$6,964.25.   Putting it together When all the components are pulled together in the final simulation, you see that the average  repair time is 2.29 days and that the copier will breakdown approximately every 4 weeks.  Due to the breakdowns and time it will take to be repaired, the company could potentially lose \$497.45  per breakdown and \$6,964.25 in total revenue.   Case Study Solution JET Copies decided that if it was determined that loss of revenue for one year was more than  \$12,000, they would need to purchase a backup copier.  According to the simulation, JET’s loss  of revenue would be \$6,964.25, a difference of \$5,035.75 less.  Therefore, it is my conclusion  that JET should not purchase the backup copier.   Using a confidence level of 95%, the upper and lower level limits are only 46.25 from the  sample mean.   We can be 95% confident that the true average loss of revenue per breakdown for the population is between \$451.20 and \$543.70.   There are several limits of the study.  First, you have to question the reliability of the information given by others of their repair times and intervals between breakdowns.  Second, you have to  look at the age of the equipment being used by those giving the information.  Since their copier  may be older and used more often, the likelihood of breakdown would be higher than that of a  new machine.  Third, the number of trials needs to be increased exponentially, to get a more  accurate representation of real­world scenarios.

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