### Application of Backflow Algorithm to a Directed GraphThis diagram represents a directed graph (digraph) with tasks (T1 to T10) and their respective processing times in parentheses. The aim is to apply the backflow algorithm to determine the critical time for specific tasks within this network.#### Diagram Overview:- **Tasks and Times**: - T1 (3) - T2 (2) - T3 (8) - T4 (11) - T5 (12) - T6 (10) - T7 (9) - T8 (4) - T9 (6) - T10 (5)- **Connections**: - The arrows indicate dependency and flow direction from one task to another. - T1 connects to T5. - T2 connects to T6. - T5 connects to T9. - Tasks T6, T8, and T10 are subsequent connections before reaching the "End". - T3 connects to T7. - T4 is a task that stands independently before reaching the "End".#### Calculating Critical Time:- **Purpose**: Calculate the critical time for Task 5 and Task 2 using the backflow algorithm.- **Formulas**: - The backward pass evaluates the longest path from end to start, determining critical times through reverse calculation from the "End" node. - Task duration and dependencies are considered to find potential delays affecting the overall project completion time.#### Critical Time Boxes:- **Task 5 Critical Time**: ________- **Task 2 Critical Time**: ________By evaluating the backward paths from each task to the "End," fill in the critical times in the designated boxes. This process aids in optimizing project schedules and identifying key dependency paths within project management scenarios.

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Description: ### Application of Backflow Algorithm to a Directed GraphThis diagram represents a directed graph (digraph) with tasks (T1 to T10) and their respective processing times in parentheses. The aim is to apply the backflow algorithm to determine the crit

The critical time for the end point is zero 0. The directly linked tasks T9, T10 and T11 have the…

Answered: Apply the backflow algorithm to the…

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Apply the backflow algorithm to the digraph below T1 (3) T5 (12) T9 (6) T2 (2) T6 (10) T8 (4) T10 (5) End Т3 (8) T7 (9) T4 (11) Task 5 has a critical time of Task 2 has a critical time of

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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### Application of Backflow Algorithm to a Directed Graph

This diagram represents a directed graph (digraph) with tasks (T1 to T10) and their respective processing times in parentheses. The aim is to apply the backflow algorithm to determine the critical time for specific tasks within this network.

#### Diagram Overview:

- **Tasks and Times**:
- T1 (3)
- T2 (2)
- T3 (8)
- T4 (11)
- T5 (12)
- T6 (10)
- T7 (9)
- T8 (4)
- T9 (6)
- T10 (5)

- **Connections**:
- The arrows indicate dependency and flow direction from one task to another.
- T1 connects to T5.
- T2 connects to T6.
- T5 connects to T9.
- Tasks T6, T8, and T10 are subsequent connections before reaching the "End".
- T3 connects to T7.
- T4 is a task that stands independently before reaching the "End".

#### Calculating Critical Time:

- **Purpose**: Calculate the critical time for Task 5 and Task 2 using the backflow algorithm.

- **Formulas**:
- The backward pass evaluates the longest path from end to start, determining critical times through reverse calculation from the "End" node.
- Task duration and dependencies are considered to find potential delays affecting the overall project completion time.

#### Critical Time Boxes:

- **Task 5 Critical Time**: ________

- **Task 2 Critical Time**: ________

By evaluating the backward paths from each task to the "End," fill in the critical times in the designated boxes. This process aids in optimizing project schedules and identifying key dependency paths within project management scenarios.

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