ASSIGMENI Problem

special class of linear Programming Problem where the objective to assign of resource $($item$)$ to an equal number of activities $($recievers$)$ on a one to one bosis so as to minimize that total cost $($or total time$)$ of Performing the tusk at hand on maximize total Profit of allocation?

Mathematical model:$-$

minimize $z={\displaystyle \underset{i=1}{\overset{n}{}}}{\displaystyle \underset{j=1}{\overset{n}{}}}{C}_{ij}{x}_{ij}$

subject to constraints

$x_{i1}+x_{i2}+$dots$+x_{in}L({}_2){\displaystyle \underset{i=1}{\overset{W}{}}}{x}_{i1}!$