= Standard maximum form of a linear program
{title2=$\max\{c^Tx:Ax\leq b,\ x\geq0\}$}
This convention for <standard maximum form of a linear program> requires a maximizing <linear function>, upper-bound <linear inequalities>, and nonnegative variables. An unrestricted variable becomes the difference of two nonnegative variables; a lower-bound inequality changes sign. The corresponding <dual linear program> is $\min\{b^Ty:A^Ty\geq c,\ y\geq0\}$. Adding nonnegative <slack variables> instead gives the equivalent equality-constraint standard form. Since standard-form terminology varies, state the chosen convention.
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