Jet Copies

Jet Copies 1

JET Copies

Strayer University

MAT 540

2

In finding the average time it takes to repair the copier, I looked at the average time which will be possible times (1-4 days) weighted by the probabilities of each. After looking at the given table, I multiplied each number of days by the probability of that number of days, and added the results to get 2.25.

The area under the diagonal line in the given graph, between two points on the x-axis, represents the probability of the copier breaking down within the times indicated by those two points. This is what we expected because we are told in the case problem that the copier will break down within six weeks.

While using the same logic to find the probability that the copier will break down between x =0 and any z. The line shown goes through (0, 0) and (6, 1/3), so it is given by y = x/18. The probability is then the area of a triangle with sizes z and z/18, or z * z/18 * ½ = z^2/36.

When you want to find the number of weeks where we have an equal probability of the copier breaking down before or after this time, this will be the average time between breakdowns. So we need z such that z^2/36 = ½. Solving gives z = 4.243 weeks.

Assuming a uniform distribution for the number of copies sold per day, so the average number of copies sold will be the average of the high and low estimates, which are 5000 copies per day. At 10 cents each, we expect revenue of $500 per day, and this amount will be lost while the copier is broken.

Jet Copies 3

Putting everything together, we find the average number of breakdowns per year to be 12.255 (dividing 52 weeks/per year by 4.243 weeks/breakdown), the revenue lost per breakdown to be $1,125 (days lost/breakdown * revenue lost/day) and the revenue lost per year due to breakdowns to be $13,787 (breakdowns/year * revenue lost/breakdown).

Jet Copies should purchase a backup copier since the revenue lost per year due to...