Who would be interested in using inequalities? what are the benefits and limitations of using inequalities to make decisions?

People creating a budget may be interested in inequalities.

Suppose you want to figure out how much money you have to spend on groceries. Your income is $100/week, and you spend $20/week on gasoline, and $30/week on clothes.
The amount x that you can spend on groceries could be written as: 
20 + 30 + x ≤ 100
Solving this:
x ≤ 50 
You can spend at most $50 on groceries.

A benefit to using inequalities to make decisions is that it helps you to establish the limitations and constraints that you are subject to. One downside, using the budget example, is that is can be difficult to determine, subject to the inequality, the exact number that you spend on groceries.
You can spend between 0 and $50 on groceries, but what amount do you choose? The inequality alone can not make that decision, and you must consider other factors to make that choice. 

The answer would be 7 cages