Question

What is the standard form of linear programming problem?

Answer 1

The standard form of linear programming problem:

• The standard form of linear programming is
  $\max z=\sum c_i{x}_i$
  Subject to $Ax=B$
  $x_i>0$
• The characteristics of a standard linear program are: 1) Maximization of a program, 2) Equality constraints and 3) non-negative variables.
• The object function of standard form of linear programming problem should be in maximization form. The minimization function could be converted into maximization function. For example min $z=-2x_1+4x_2$ is equivalent to $max{z}^{*}=2x_1-4x_2$.
• All constraints can be converted into an equation.

1. The inequality $3x_1+7x_2\ge 40$ can b written as $3x_1+7x_2-s_1=40$, where $s_1$ is called surplus variable.
2. The inequality $7x_1-2x_2\le 4$ can b written as $7x_1-2x_2+s_2=4$, where $s_2$ is called slack variable.