A small company wants to give raises to their 5 employees. They have \(10,000 available to distribute. Imagine you are in charge of deciding how the raises should be determined.
The answer here depends on your definition of fairness. In method 2 everybody gets the same percent raise. So if you have a high salary, you get a larger pay raise than if you have a lower salary. This is probably the method used most commonly.
If your goal is to support lower paid employees, then method 3 is designed to accomplish this. Here the raise rewards number of hours worked and it does not depend on your salary at all. So lower paid employees receiver a larger percent raise than higher paid employees.
Method 1 is probably the least fair by most definitions, since no matter how much you work, you receive the same raise. A person working few hours or earning a smaller salary would receive a much higher percent raise than a person working many hours or earning a higher salary.
Commentary
This is foremost a mathematical modeling task. The task very specifically asks to discuss the variables that could be important in finding a mathematical method for determining raises. This step is often neglected in textbook problems but it is not easy and not at all obvious to students.
There are many factors that go into giving raises: Does everybody get the same raise or do different people get different raises? And if everybody gets the same raise, what does that mean? Do they are get the same dollar amount or do they all get the same percent raise?
The matter of fairness will certainly come up in this task. But what does that mean? New questions may come up: Does every employee work full time or do some of them work part time?
The instructor may choose to have students ask for information and then supply this information. For example: Students may ask for the salary of each employee and if they are full time or part time (whatever that may mean). Employees might have different education (HS, college, post-graduate degree) and they may have different seniority.