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11 A project involves 13 tasks; the tasks, their estimated duration, and their immediate predecessors are shown in the table below: Immediate Task predecessors Duration Task 1 1 Task 2 1 2 Task 3 3 Task 4 4 Task 5 1 2 Task 6 2.3 1 Task 7 4 2. Task 8 5 6 Task 9 5 10 Task 10 6.7 5 Task 11 8,10 3 Task 12 8.10 3 Task 13 12 2 Our objective is to find the schedule of tasks that minimizes the total elapsed time of the project. a) Draw the task- and event-oriented networks for this problem. b) Formulate the corresponding linear program (both task and event-oriented networks). c) Solve the event-oriented LP by LPsolver (R codes). 11 A project involves 13 tasks; the tasks, their estimated duration, and their immediate predecessors are shown in the table below: Immediate Task predecessors Duration Task 1 1 Task 2 1 2 Task 3 3 Task 4 4 Task 5 1 2 Task 6 2.3 1 Task 7 4 2. Task 8 5 6 Task 9 5 10 Task 10 6.7 5 Task 11 8,10 3 Task 12 8.10 3 Task 13 12 2 Our objective is to find the schedule of tasks that minimizes the total elapsed time of the project. a) Draw the task- and event-oriented networks for this problem. b) Formulate the corresponding linear program (both task and event-oriented networks). c) Solve the event-oriented LP by LPsolver (R codes)