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:

    “An indirect quotation we can usually expect to rate only as better or worse, more or less faithful, and we cannot even hope for a strict standard of more and less; what is involved is evaluation, relative to special purposes, of an essentially dramatic act.”
    —Willard Van Orman Quine (b. 1908)

    “It is a conquest when we can lift ourselves above the annoyances of circumstances over which we have no control; but it is a greater victory when we can make those circumstances our helpers,—when we can appreciate the good there is in them. It has often seemed to me as if Life stood beside me, looking me in the face, and saying, “Child, you must learn to like me in the form in which you see me, before I can offer myself to you in any other aspect.””
    —Lucy Larcom (1824–1893)