An electrical contractor pays his subcontractors a fixed fee plus mileage for work performed. On a given day the contractor is faced with three electrical jobs associated with various projects. Each subcontractor will have enough time to work on up to two projects during the day. Each project should be completed by exactly two subcontractors. Given below are the distances between the subcontractors and the projects

$\backslash$table$[[,$Projects$],[$Subcontracto$,$A$,$B$,$C$],[$r$,,,],[$Westside$,2,3,4],[$Federated$,6,1,5],[$Goliath$,5,6,6],[$Universal$,11,2,3]]$

a$.$ Draw a network to represent the possible subcontractor$-$project assignments.

b$.$ Develop a linear model which would be used to minimize total mileage costs.