Consider the following mathematical program.

Assume that $s_i$ and $d_j$ are integer and non$-$negative.

Minimize: $z={\displaystyle \underset{i=1}{\overset{m}{}}}{\displaystyle \underset{j=1}{\overset{n}{}}}{c}_{ij}{x}_{ij}$

Subject to:

${\displaystyle \underset{j=1}{\overset{n}{}}}{x}_{ij}=s_i,$AAi$=1,$dots,$m$

${\displaystyle \underset{i=1}{\overset{m}{}}}{x}_{ij}=d_j,$AAj$=1,$dots,$n$

$x_{ij}0,$

Indicate which solution methodology discussed in class you would use to solve the problem. Justify your answer. You do not have to solve the problem, merely state how you would solve the problem.