Applications of Linear Inequalities

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:

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.

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

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.

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

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