Linear Programming - Augmented Form (slack Form)

Augmented Form (slack Form)

Linear programming problems must be converted into augmented form before being solved by the simplex algorithm. This form introduces non-negative slack variables to replace inequalities with equalities in the constraints. The problem can then be written in the following block matrix form:

Maximize Z:
 \begin{bmatrix} 1 & -\mathbf{c}^T & 0 \\ 0 & \mathbf{A} & \mathbf{I} \end{bmatrix} \begin{bmatrix} Z \\ \mathbf{x} \\ \mathbf{x}_s \end{bmatrix} = \begin{bmatrix} 0 \\ \mathbf{b} \end{bmatrix}
x, xs ≥ 0

where xs are the newly introduced slack variables, and Z is the variable to be maximized.

Read more about this topic:  Linear Programming

Famous quotes containing the words augmented and/or form:

    Another success is the post-office, with its educating energy augmented by cheapness and guarded by a certain religious sentiment in mankind; so that the power of a wafer or a drop of wax or gluten to guard a letter, as it flies over sea over land and comes to its address as if a battalion of artillery brought it, I look upon as a fine meter of civilization.
    Ralph Waldo Emerson (1803–1882)

    I can’t work without a model. I won’t say I turn my back on nature ruthlessly in order to turn a study into a picture, arranging the colors, enlarging and simplifying; but in the matter of form I am too afraid of departing from the possible and the true.
    Vincent Van Gogh (1853–1890)