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:

    “Society’s double behavioral standard for women and for men is, in fact, a more effective deterrent than economic discrimination because it is more insidious, less tangible. Economic disadvantages involve ascertainable amounts, but the very nature of societal value judgments makes them harder to define, their effects harder to relate.”
    —Anne Tucker (b. 1945)

    “A criminal trial is like a Russian novel: it starts with exasperating slowness as the characters are introduced to a jury, then there are complications in the form of minor witnesses, the protagonist finally appears and contradictions arise to produce drama, and finally as both jury and spectators grow weary and confused the pace quickens, reaching its climax in passionate final argument.”
    —Clifford Irving (b. 1930)