Suppose that the average time before breakdown is normally distributed with a mean of 2.5 weeks and a standard deviation of .4 weeks. If breakdowns cost an average of $1,200 and preventive maintenance costs $800, what is the optimal maintenance interval?
A)Every .67 weeks
B)Every .33 weeks
C)Every 2.67 weeks
D)Every 3.25 weeks
E)Every 3.12 weeks

Question

Quizplus · Accepted Answer

The optimal maintenance interval minimizes the total expected cost, which includes both the cost of breakdowns and the cost of preventive maintenance. The expected cost function, given a maintenance interval $T$, is $C(T) = \frac{1200}{T} + 800$, where $\frac{1200}{T}$ represents the expected cost of breakdowns per week and $800$ is the cost of preventive maintenance per interval. The interval that minimizes this cost will be close to the mean time before breakdown (2.5 weeks) because performing maintenance too frequently increases the maintenance cost without significantly reducing the breakdown cost, and waiting too long increases the breakdown cost. Among the given options, every 2.67 weeks (C) is the closest to the mean and represents a reasonable balance between the costs.

Suppose That the Average Time Before Breakdown Is Normally Distributed