Problem $7($Adapted from Winston, $2004).$ Bob is currently building three homes, and he needs to

schedule five contractors to complete tasks at each of the homes. The number of days required for each

contractor to complete the work at each home is given in the following table:

In creating the schedule, Bob wishes to ensure the following:

For each home, excavation is performed first, followed by foundation, framing, plumbing, and

roofing $($in order$).$

There is only one contractor of each type $($excavation$,$ foundation, framing, plumbing, and

roofing$).$ Each contractor can work on only one home at a time. A contractor's work on one

home must be completed before it can begin working on another home.

Part a: Formulate an integer$-$linear program to determine a schedule that minimizes the number of days

until the last home is completed.

Part b: Solve the problem using AMPL$/$CPLEX and report the obtained optimal solution.