State Irrigation Corporation $($S$.$IC$.)$ is a state government organization of various irrigation projects in the state. S$.$L$.$C$.$ normally gets all the jobs done through contractors under its overall supervision. One of the jobs awarded to a relatively small contractor relates to the Head Regulator of Right bank Main Canal $($RBMC$)$ of a medium size irrigation project. The various activities and the details of these activities as identified by the contractor are as follows:

$\backslash$table$[[$Activities$,$Description,Dependence,Duration $($Weeks$)],[$A$,$Foundation Concrete,$-,2],[$B$,$UCR Masonry $1$:$5,$A$,3],[$C$,$UCR Masonry $1$:$3,$A$,4],[$D$,$Coping,B$,$C$,2],[$E$,$Concrete for stilling Basin,B$,$C$,3],[$F$,$Complete stilling Basin,D$,$E$,3],[$G$,$Control Well and Fort Bridge,D$,$E$,5],[$H$,$Erect Trash Racks and Gates,F$,3],[$I$,$Final Inspection & Testing,G$,$H$,2]]$

Due to concern for quality performance S$.$I.C$.$ insisted that all activities are closely supervised and inspected by personnel $($Supervisors$)$ to be appointed by the contractors but approved by S$.$I.C$.$ Due to temporary nature of the job and requirement of higher standards, resulted in appointment of only $5($Five$)$ supervisors by the contractor. The req