1. Applications of Linear Inequalities

2. Keep the following phrases in mind:
Many real-life situations can be dealt with using systems of linear inequalities.
Proper use of inequalities symbols is crucial.
Keep the following phrases in mind:

3. At most a certain quantity indicates
That means we can use that quantity or less.
At least a certain quantity indicates
That means we can use that quantity or more.
A certain quantity is needed indicates
That means we should have that quantity or more.
A certain quantity is available indicates That means we could use that quantity or less.

5. Let x be the number of units of A produced and y the number of units of B produced.
We have the system
of linear inequalities:
The profit is given by

6. Note that we did not answer the question
“How many units of product A and how many units of product B will give a profit as big as possible?”
We now need to sharpen our ability to convert a a given real-life problem in to a system of inequalities.

8. Let x be the number of pills of brand X and y the number of pills of brand Y.
We obtain the system
of linear inequalities
The cost C (in cents) is given by

9. What did we gain from the two examples considered?
They show that linear inequalities can be used to described real-life problems
They prepare us for the study of
Linear Programming