Problem 2 ARC Consultants needs to know how long it will take to complete a particular job. The job consists of n different tasks. Each task k takes t hours to complete (regardless of how many people work on it). Additionally, certain tasks cannot be performed until other tasks have been completed. This information is represented in a nxn matrix P where the (i, j)th element of the matrix is a 1 if task j must be performed before task i and a 0 otherwise. (Note that all elements on the diagonal must be zero as a task cannot be performed before itself.) There is no limit on the number of tasks that can be performed at once.
Set up a linear program that determines how soon ARC can complete the job. As always, clearly specify your decision variables, objective function and constraints.