The Simplex method is an algorithm that solves linear programming problems with three or more variables. It is highly efficient and used in business, science, and industry in a variety of scenarios.

## History

The Simplex method was an invention of Dr. George Dantzig in 1947, a replacement for other methods of solving linear programming problems. It effectively replaced them due to its power and efficiency.

## Benefits

For complex problems involving many variables, the Simplex method is much faster than other algorithms at solving linear systems. The Simplex method's efficiency is important for computer programming, as the need for processing power is significantly lower when using it.

## Significance

If more than three variables are in the problem, graphical methods will fail, as dimensions over 3 cannot be visualised using them. The Simplex method can apply where graphical methods can't.

## Function

The Simplex method necessitates taking a set of vertices and testing them with adjacent vertices, until none are left to test. In the method you use two states. Either the function improves or remains unchanged. Any other change is ignored.

- The Simplex method necessitates taking a set of vertices and testing them with adjacent vertices, until none are left to test.
- Either the function improves or remains unchanged.

## Usage

If a system is comprised of entities whose behaviour can be modelled with a linear function, you can employ the Simplex method. Systems appropriate for the Simplex method include numerous applications in economics, such as optimising the price given supply and demand, or in science, monitoring predators and prey in a given environment.