Nothing: Random Variable and Jet Copies Essay

JET Copies – Case Description
University students James, Ernie and Terri are opening a new copy center business called JET Copies. They borrowed $18,000 from Terrie’s parents to purchase their main copy machine. After the copy machine was purchased Ernie found out from a friend that the copy machine had frequent breakdowns; a breakdown between 1 and 6 weeks and often took 1 – 4 days for repair. In order to keep the business running between repairs the business owners are evaluating whether to purchase an $8,000 back up copy machine. The owners decided that if revenue lost per year was greater than $12,000 the additional copier purchase would be made.
JET Copies’ owners are putting together a simulation model to determine whether the purchase of another copy machine is necessary. They have the following information:
• Time between breakdowns is 1- 6 weeks with probability of a breakdown increasing the longer the copier went without a breakdown
• repair time probabilities
Table 1: Probability of the days to repair copier
Repair Time (days) Probability
1 0.20
2 0.45
3 0.25
4 0.10
• Loss of revenue during repair of the copier: approx. 2000 – 8000 copies/day at $0.10/copy
Again, if revenue lost/year was greater than $12,000 then the purchase of a second copier would be warranted. A simulation model using MicroSoft Excel was run to determine lost revenue due to copier breakdowns.
To compute the simulation analysis we will run 1000 random numbers (trials) in a MicroSoft Excel spreadsheet and determine: interval between successive copier breakdowns, the number of days needed to repair the copier using the probabilities in Table 1, and the lost revenue for each day the copier is out of service and then the lost revenue per year.
To compute the number of days between breakdowns, a continuous probability distribution (probability (0 ≤ X ≤ 6)), was run using 1000 random numbers between 0 – 6 weeks. Since the numbers between 0 and 6 are infinite the value X in the continuous random variable calculation was generated by Excel, and then calculated by using the formula is: Pr[0 ≤ X ≤6] = x = standard deviation of the random number x 6 weeks. The result of 1000 random numbers estimated that a copier breakdown would occur once every four (4) weeks.
Next the owners of JET copies have to determine how long it would take to get the copier repaired. The owners did some initial research and came up the set of probabilities it would take to get the copier repaired (Table 1). Again a continuous probability was used in Excel using 1000 random numbers to determine how long it will take to repair the copier based on the probabilities considered in Table 1. The program estimated it would take 2.17 days to get the copier repaired.
The main question posed by the owners is how much revenue would be lost during the copier breakdown/repair process. JET Copies owners determined that the range of sales per day is between 2000 and 8000 copies/day at $0.10/copy. The potential loss with the copier down for two (2) days could be between $400 – 1600 dollars/2 days. However, to get a better understanding of the exact amount of revenue lost another simulation model was run using a uniform probability distribution. To calculate this distribution the formula: X = 2000 + (8000-2000 x a random number (r)) was used in the excel spreadsheet for a 1000 trials. The simulation model calculated that 4948 copies/day or 11,000 copies/2 days, could be lost during the copier breakdown/repair process out

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