Excerpt $2$:

Since any LP$-$model can be reformulated to be in standard form

Maxz$=c_1{x}_1+$dots$+c_n{x}_n$

with

$a_{11}{x}_1+$dots$+a_{1n}{x}_n=,b_1$

$*,*$

${*}^{},*$

$a_{m1}{x}_1^{}+$dots$+a_{mn}{x}_n=,b_m^{}$

$.4\mathrm{.}1)$

and

$x_{1}0,$dots,$x_{n}0$

or in the canonical form

Maxz$=c_1{x}_1+$cdots$+c_n{x}_n$

with

$a_{11}{x}_1+$dots$+a_{1n}{x}_n{b}_1$

$*$

$*$

$a_{m1}{x}_1^{}+$dots$+a_{mn}{x}_n{b}_m^{}$

$q,(4\mathrm{.}2)$

and

$x_{1}0,$dots,$x_{n}0$

these two forms are often the starting point for solution procedures. But before we come to that we must explore the methods by which an LP$-$model can be reformulated to assume the standard or the canonical form.