Simplex algorithm is one of the methods to solve linear programming problems.

It solves the standard form of linear programming problem: Maximizing $c^T . x$ subject to $Ax = b$ all $x_i >= 0$ and all $b_j >= 0$ .

Where:

c = coefficients
x = the variables
A = a rectangular matrix
b = constants

Simplex algorithm iteratively tests adjacent vertices all the while improving the objective function. This can also be visualized as a traversal along the edges of a polytope formed by the standard form.