Linear Programming - Standard Form

Standard form is the usual and most intuitive form of describing a linear programming problem. It consists of the following three parts:

A linear function to be maximized

e.g.

Problem constraints of the following form

e.g.

$\begin{matrix} a_{11} x_1 + a_{12} x_2 &\leq b_1 \\ a_{21} x_1 + a_{22} x_2 &\leq b_2 \\ a_{31} x_1 + a_{32} x_2 &\leq b_3 \\ \end{matrix}$

Non-negative variables

e.g.

$\begin{matrix} x_1 \geq 0 \\ x_2 \geq 0 \end{matrix}$

The problem is usually expressed in matrix form, and then becomes:

Other forms, such as minimization problems, problems with constraints on alternative forms, as well as problems involving negative variables can always be rewritten into an equivalent problem in standard form.

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