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2. Create a digraph for the following set of tasks: Task Time required A B C D E F G 3 4 7 6 5 5 4 Tasks that must be completed first A A B D, E

2. Create a digraph for the following set of tasks: Task Time required A B C D E F G 3 4 7 6 5 5 4 Tasks that must be completed first A A B D, E

Advanced Engineering Mathematics
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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Contemporary Mathematics 

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### Task Dependency Digraph **Objective:** Create a digraph for the given set of tasks, emphasizing task dependencies. #### Task Information: | Task | Time Required | Tasks That Must Be Completed First | |------|---------------|------------------------------------| | A | 3 | | | B | 4 | | | C | 7 | | | D | 6 | A | | E | 5 | A | | F | 5 | B | | G | 4 | D, E | #### Explanation: To construct a digraph from the table above, follow these steps: 1. **Identify Tasks without Dependencies:** - Tasks A, B, and C have no prerequisites and can be started immediately. 2. **Identify Tasks with Dependencies:** - Task D requires completion of Task A. - Task E requires completion of Task A. - Task F requires completion of Task B. - Task G requires completion of both Tasks D and E. 3. **Graph Construction:** - Represent each task as a node. - Use directed edges (arrows) to show dependencies between tasks: - Arrow from A to D and E (A must be completed before D and E can start). - Arrow from B to F (B must be completed before F can start). - Arrows from D and E to G (Both D and E must be completed before G can start). This digraph visually explains the sequence and prerequisites for each task, aiding in efficient project planning and management.
Transcribed Image Text:### Task Dependency Digraph **Objective:** Create a digraph for the given set of tasks, emphasizing task dependencies. #### Task Information: | Task | Time Required | Tasks That Must Be Completed First | |------|---------------|------------------------------------| | A | 3 | | | B | 4 | | | C | 7 | | | D | 6 | A | | E | 5 | A | | F | 5 | B | | G | 4 | D, E | #### Explanation: To construct a digraph from the table above, follow these steps: 1. **Identify Tasks without Dependencies:** - Tasks A, B, and C have no prerequisites and can be started immediately. 2. **Identify Tasks with Dependencies:** - Task D requires completion of Task A. - Task E requires completion of Task A. - Task F requires completion of Task B. - Task G requires completion of both Tasks D and E. 3. **Graph Construction:** - Represent each task as a node. - Use directed edges (arrows) to show dependencies between tasks: - Arrow from A to D and E (A must be completed before D and E can start). - Arrow from B to F (B must be completed before F can start). - Arrows from D and E to G (Both D and E must be completed before G can start). This digraph visually explains the sequence and prerequisites for each task, aiding in efficient project planning and management.
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