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.

Read more about this topic:  Linear Programming

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