Linear Programming: Optimizing with Inequalities [Art of Problem Solving Intro to Algebra 9.40]
If you're a student who likes to ask "when am I ever gonna use this in real life?", then linear programming is the topic for you. Businesses actually do this kind of process every single day.
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Linear programming, also sometimes called linear optimization, is all about maximizing or minimizing some quantity given certain constraints, limitations, or restrictions. Today, I want to take a look at the process by working through an example from the Art of Problem Solving Introduction to Algebra textbook. The problem is 9.40.
There are three main questions you want to ask yourself as you model these scenarios:
1) What are the constraints
2) What do we NOT know?
3) What is the objective?
Unlike a system of equations, for linear programming, you don't really want to solve it algebraically. Instead, you want to set up your linear inequalities, then graph those inequalities. The region of possible solutions will have some number of "corners", and it is those points that you check in your objective equation.
#linearprogramming #linearoptimization #artofproblemsolving
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