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Mathematics

Secondary 5 • January 10, 2025

Hello! I’m doing the critical path method (optimization) right now and I can’t seem to understand the first step : represent the situation using a weighted and directed graph….
I do know what a weighted and directed graph is but I don’t understand how to represent the situation using a weighted and directed graph.
im using alloprof concept sheet (CST math)

thank you! :)

Answer (1)

Alloprof Answer

January 11, 2025

Hello SuperbStrawberry8290,
Thank you for your question!
A weighted graph is a type of graph where weights are assigned to each edge. A directed graph is a graph that shows the direction of paths. Each edge has an arrow indicating its direction.
This is an example of a weighted and directed graph. As you can see, there are different dots, which represent different "steps." For example, you need to complete step A before moving on to step B. This setup represents a series of actions required to accomplish the goal. Each number above the arrows represents the weight, which is the time needed to complete the task.
Capture d’écran, le 2025-01-10 à 22.08.44.png

Capture d’écran, le 2025-01-10 à 22.08.44.png

Here, you can see that task A takes one day to complete. Task B also takes one day. Between B and F, there are multiple paths.
The critical path is the path with the highest total weight. To identify it, you need to add the weights of each step along the paths and compare the totals.
I hope this helps!
Laurie