The basics of linear programming

Linear Programming (LP) algorithms are adopted in all those areas where optimization, and therefore the economy of resources, is critical to the continuation of activities. In order to understand what this is all about, you need some math. Let's brush up on some of the geometric concepts we encountered during our youthful studies.

Linear equations and inequalities

We all at least once in our lives have encountered the term linear equation. A linear equation, in its simplest sense, consists of a mathematical relationship between two variables, x and y, in the form ax + by + c = 0, which on the Cartesian plane identifies a straight line:

Figure 10.14 – Representation of the linear equation 2x + y = 2

Evidently, the variables involved in a linear equation can be more than two. The representation of a linear equation is possible as long as we have three variables (the famous three dimensions we can see). In this...