Linear programming
Augmented form (slack form)

Linear programming problems can be converted into an augmented form in order to apply the common form of the simplex algorithm. This form introduces non-negative slack variables to replace inequalities with equalities in the constraints. The problems can then be written in the following block matrix form:

where s {\displaystyle \mathbf {s} } are the newly introduced slack variables, x {\displaystyle \mathbf {x} } are the decision variables, and z {\displaystyle z} is the variable to be maximized.
combination:two_responses, oulipo:avoid_letter[t], startend:quotation