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:

    “Liberty requires opportunity to make a living—a living decent according to the standard of the time, a living which gives a man not only enough to live by, but something to live for.”
    —Franklin D. Roosevelt (1882–1945)

    “Mine eye hath play’d the painter, and hath steel’d
    Thy beauty’s form in table of my heart:”
    —William Shakespeare (1564–1616)