Jet Copies Case Problem

Math 540

4/27/2013

JET Copies Case Problem

James, Terri and Ernie liked the idea of opening a business making copies. They would call it JET Copies, named for James, Ernie, and Terri. Their first step was to purchase a copier. They bought one like the one used in the college of business office at State for $18,000. (Terri’s parents provided a loan.) The company that sold them the copier touted the copier’s reliability, but after they bought it, Ernie talked with someone in the dean’s office at State, who told him that the University’s copier broke down frequently and when it did, it often took between 1 and 4 days to get it repaired.

In this case study James, Terri and Ernie should have taken into consideration what the longevity was on the copier. James and Ernie should have listened to Terri and purchased a smaller backup copier for $8,000 to use when the main copier broke down.

The reason for the need of a backup copier is because there was a big lost in revenue. James, Ernie, and Terri should have decided to purchase a machine because the downtime during 1 year was a major lost after calculations.

In a summary always do a data analysis along with your business plan before purchasing large quantity items.

1. If you assume that the number of days needed to repair a copier is random you can generate a random number using the Excel RAND function which I denoted r2 between 0 and 1. If

0 < r2 < 0.2 Then it takes 1 day

0.02 < r2 < 0.65 Then it takes 2 days

0.65 < r2 < 0.90 Then it takes 3 days

0.9 < r2 < 1 Then it takes 4 days

2. The probability distribution of the random variable varies between the times of 0 to 6 weeks, with the probability increasing as time goes on. This can be approximated by the function

F(x) =x/18 for 0< x < 6

Therefore the distribution function is

F(x) = For 0 < x < 6

If we set this equal to another random number r1 that is between 0 and 1 then

r1 = x = 6

3. Since the number of copies sold per day is a uniform probability distribution between 2000 to 8000 copies, I made r3 a random number between 2000 and 8000. To get the amount of business lost on a particular day I take r3 x (repair time), and the lost revenue is then equal to since they charge $0.10 per copy.