$($Assignment Model$)$ Torres y Comunicaciones Beta, Inc. sells and installs floor coverings for commercial buildings. Camilo Serrac$$n$,$ an account executive, has just won a contract for five jobs. Camilo must assign a group of Torres y Comunicaciones Beta, Inc. installation personnel to each of the five jobs. Since the commission that Camilo will earn depends on the profits that Torres $y$ Comunicaciones Beta, Inc. earns, Camilo would like to determine an assignment that minimizes the total installation cost. Currently, five installation groups are available for assignment. Each group is identified by a color code, which helps track the progress of the job on a large whiteboard. The following table shows the costs $($in hundreds of dollars$)$ for each group to complete each of the five jobs:

$\backslash$table$[[$GRUPO$,$Trabajo $1,$Trabajo $2,$Trabajo $3,$Trabajo $4,$Trabajo $5],[$Amarillo$,35,40,37,46,35],[$Azul$,20,30,50,45,30],[$Rojo$,24,45,38,40,25],[$Verde$,27,39,38,44,22],[$Naranja$,27,32,45,40,22]]$

Color code are in Spanish

a$)$ Develop a network representation for this problem.

b$)$ Formulate a linear programming model of the problem.