(b) A company needs to schedule the following tasks (shown in Table 2), numbered from 1 to 7, each of which has a duration and a list of prerequisite tasks that need to have been completed before they are started. For example, Task 4 will take 10 hours and needs Tasks 2 and 3 to be over before it is taken up. Prerequisites None Task Task 1 Duration 8 hrs Task 2 4 hrs Task 1 Task 3 3 hrs Task 1 Task 4 10 hrs Tasks 2, 3 Task 5 5 hrs Task 2 Task 6 4 hrs Task 3 Task 7 3 hrs Tasks 4, 5, 6 Table 2: The tasks and their details. Let ti be a decision variable that signals the starting time of Task i, and assume that there is a fake "starting task", Task 0, with a duration of 0 hours, that starts at time 0, and a fake ending task", Task 8, with a duration of 0 hours, and a starting time of t8. Clearly, the smallest the time to the earliest the ending of the overall project, so our problem would have the goal of min t8. Formulate the problem of minimizing the duration of the whole project, while satisfying all the prerequisite requirements. Then, using the theory discussed during Lecture 10, formulate its dual. Can it be written as a shortest path problem? And, if so, recommend a method that solves the