### Project Scheduling with Directed Acyclic Graphs (DAG)#### Task Scheduling Using a Priority List**Objective**: Schedule the project using two processors based on the priority list.**Priority List**: T₆, T₄, T₉, T₅, T₁₀, T₇, T₁, T₃, T₈, T₂#### Task Diagram ExplanationThe diagram is a Directed Acyclic Graph (DAG) representing tasks and their dependencies in a project:- **Nodes (Tasks)**: Each node represents a task, labeled T₁ to T₁₀. The numbers in parentheses next to each task indicate the time units required to complete the task (e.g., T₁ (12) takes 12 time units).- **Arrows (Dependencies)**: Arrows between tasks show the dependency order. A task at the start of an arrow must be completed before the task at the end of the arrow can begin.- **Nodes to Complete the Project**: Start and End nodes indicate the beginning and completion of the project.#### Task List and Times- **T₁ (12)**: Requires 12 units- **T₂ (9)**: Requires 9 units- **T₃ (10)**: Requires 10 units- **T₄ (8)**: Requires 8 units- **T₅ (7)**: Requires 7 units- **T₆ (2)**: Requires 2 units- **T₇ (6)**: Requires 6 units- **T₈ (11)**: Requires 11 units- **T₉ (5)**: Requires 5 units- **T₁₀ (3)**: Requires 3 units#### Scheduling Task with Processors- **Processor Assignment**: Tasks must be assigned to two processors based on the priority list order. - Task 7 (T₇) is assigned to Processor 1. - Task 8 (T₈) is assigned to Processor 1.**Instructions**: Enter the start time for each task performed by the processor in the provided input fields. Tasks must adhere to dependencies before initiation.

Task 7 is done by processor 1 starting at time 27 hours. Processor 1: T1, T4, T5, T7, T10, T6

Answered: Using the priority list T6, T4, T9, T5,…

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Using the priority list T6, T4, T9, T5, T10, T7, T1, T3, Tg, T2, schedule the project below with two processors.

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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Question

### Project Scheduling with Directed Acyclic Graphs (DAG)

#### Task Scheduling Using a Priority List

**Objective**: Schedule the project using two processors based on the priority list.

**Priority List**: T₆, T₄, T₉, T₅, T₁₀, T₇, T₁, T₃, T₈, T₂

#### Task Diagram Explanation

The diagram is a Directed Acyclic Graph (DAG) representing tasks and their dependencies in a project:

- **Nodes (Tasks)**: Each node represents a task, labeled T₁ to T₁₀. The numbers in parentheses next to each task indicate the time units required to complete the task (e.g., T₁ (12) takes 12 time units).
- **Arrows (Dependencies)**: Arrows between tasks show the dependency order. A task at the start of an arrow must be completed before the task at the end of the arrow can begin.
- **Nodes to Complete the Project**: Start and End nodes indicate the beginning and completion of the project.

#### Task List and Times

- **T₁ (12)**: Requires 12 units
- **T₂ (9)**: Requires 9 units
- **T₃ (10)**: Requires 10 units
- **T₄ (8)**: Requires 8 units
- **T₅ (7)**: Requires 7 units
- **T₆ (2)**: Requires 2 units
- **T₇ (6)**: Requires 6 units
- **T₈ (11)**: Requires 11 units
- **T₉ (5)**: Requires 5 units
- **T₁₀ (3)**: Requires 3 units

#### Scheduling Task with Processors

- **Processor Assignment**: Tasks must be assigned to two processors based on the priority list order.

- Task 7 (T₇) is assigned to Processor 1.
- Task 8 (T₈) is assigned to Processor 1.

**Instructions**: Enter the start time for each task performed by the processor in the provided input fields. Tasks must adhere to dependencies before initiation.

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