A construction project involves 13 tasks; the tasks, their estimated duration, and their immediate predecessors are shown in the table below:

Our objective is to find the schedule of tasks that minimizes the total elapsed time of the project.

 a) Draw the event- and task-oriented networks for this problem and formulate the corresponding linear program.

 b) Solve to find the critical path.

Immediate Task predecessors Duration Task 1 Task 2 Task 3 Task 4 Task 5 Task 6 Task 7 Task 8 Task 9 Task 10 Task 11 Task 12 Task 13 1 TI 1 2,3 4 5 5 6,7 8,10 8,10 12 1 2 3 4 2 1 2 6 10 5 3 32 3 2