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:

    “Gentlemen, those confederate flags and our national standard are what has made this union great. In what other country could a man who fought against you be permitted to serve as judge over you, be permitted to run for reelection and bespeak your suffrage on Tuesday next at the poles.”
    —Laurence Stallings (1894–1968)

    “In full view of his television audience, he preached a new religion—or a new form of Christianity—based on faith in financial miracles and in a Heaven here on earth with a water slide and luxury hotels. It was a religion of celebrity and showmanship and fun, which made a mockery of all puritanical standards and all canons of good taste. Its standard was excess, and its doctrines were tolerance and freedom from accountability.”
    —New Yorker (April 23, 1990)