linear programming

Linear programming is a method for optimization in a mathematical model whose requirements are linear relationships.

In canonical form:

Maximize or minimize $\mathbf{c}^\mathrm{T} \mathbf{x}$ subject to $\mathbf{A} \mathbf{x} \le \mathbf{b}$ and $\mathbf{x} \ge \mathbf{0}$

where $\mathbf{x}$ is a vector of variables, $\mathbf{b}$ and $\mathbf{c}$ are known vectors, and $\mathbf{A}$ is a known matrix.