Explore BrainMass
Share

Auto Insurance Percentage of Coverage

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

An auto insurance company classifies its customers in three categories: poor, satisfactory, and preferred. Each year, 30% of those in the poor category are moved to satisfactory and 5% of those in the satisfactory category are moved to preferred. Also, 5% of those in the satisfactory category are moved to the poor category. Customers are never moved from poor to preferred, or conversely, in a single year. Assuming these percentages remain valid over a long period of time, how many customers can the company expect to have in each category in the long run?

Poor =
Satisfactory =
Preferred =

© BrainMass Inc. brainmass.com October 10, 2019, 2:17 am ad1c9bdddf
https://brainmass.com/math/discrete-optimization/auto-insurance-percentage-coverage-370651

Solution Preview

In the long run, we should expect that the total number in each category remains constant. Let's say that in the long run, there are a poor, b satisfactory and c preferred. We immediately establish the following points,

-30% of poor goes to satisfactory (poor category becomes 0.7a, satisfactory becomes b+0.3a)

-5% satisfactory moves to preferred ...

Solution Summary

This solution helps with a problem that explains how many customers a company can expect to have in various satisfaction categories.

\$2.19