Math Problem Statement

Create a digraph for the following set of tasks based on their dependencies and time requirements.

Solution

The image contains a task table, and the goal is to create a digraph for the tasks based on the dependencies listed.

Extracted Information from the Table

  • Tasks and Time Required
    • A: Time 3
    • B: Time 4
    • C: Time 7
    • D: Time 6 (requires A, B)
    • E: Time 5 (requires B)
    • F: Time 5 (requires D, E)
    • G: Time 4 (requires E)

Steps to Create the Digraph

  1. Vertices: Represent the tasks (A, B, C, D, E, F, G) as nodes.
  2. Edges: Create directed edges from prerequisite tasks to the dependent tasks.
    • For example, there will be edges from A → D and B → D since D depends on A and B.

Resulting Digraph Representation

Edges based on dependencies:

  • A → D
  • B → D
  • B → E
  • D → F
  • E → F
  • E → G

The resulting digraph will visually illustrate these connections with arrows showing dependencies.


Next Steps

Would you like me to:

  • Create a textual representation (adjacency list or matrix)?
  • Generate a drawn diagram of the digraph for you?
  • Solve any scheduling or path-related question (like critical path analysis)?

Let me know!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Graph Theory
Directed Graphs
Task Dependency Analysis

Formulas

Graph adjacency representation

Theorems

Basic graph theory properties

Suitable Grade Level

Grades 10-12