A linear programming of linear functions deals with

Minimize $z=\sum _{j=1}^n\sum _{i=1}^m{c}_{ij}{x}_{ij}$ 

Subject to$\sum _{j=1}^n{x}_{ij}=a_i, i=1, \dots , m$ 

$\sum _{i=1}^m{x}_{ij}=b_j, j=1, \dots , n$ is a $\mathrm{LPP}$ with number of constraints

The constraints

$-x_1+x_2\le 1$

$-x_1+3x_2\le 9$

$x_1, x_2\ge 0$ defines a