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

Famous quotes containing the words standard and/or form:

“The urge for Chinese food is always unpredictable: famous for no occasion, standard fare for no holiday, and the constant as to demand is either whim, the needy plebiscite of instantly famished drunks, or pregnancy.”
—Alexander Theroux (b. 1940)

“The legislator should direct his attention above all to the education of youth; for the neglect of education does harm to the constitution. The citizen should be molded to suit the form of government under which he lives. For each government has a peculiar character which originally formed and which continues to preserve it. The character of democracy creates democracy, and the character of oligarchy creates oligarchy.”
—Aristotle (384–323 B.C.)