Five different jobs are waiting to be processed on three machines, $A,B$ and $C($Recall the Johnson's Algorithm from IE $302.$ Each task has to be processed on those machines with the given order $($first $A,$ then $B,$ and finally, $C).$ Formulate a mathematical model that determines the optimal sequencing of the jobs in order to minimize makespan $($finish time of the last job$).$

Table $1$: Task Information

$\backslash$table$[[$Job$,$A$,$B$,$C$],[1,6,2,11],[2,2,7,7],[3,5,4,5],[4,9,5,13],[5,7,8,8]]$