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The network diagram shows the time needed for each step in order to complete a project - HSC - SSCE Mathematics Standard - Question 3 - 2022 - Paper 1
Question 3
The network diagram shows the time needed for each step in order to complete a project. 3 3 C, 13 16 20 A, 3 --> D, 16 --> G, 1 2 0... show full transcript
Worked Solution & Example Answer:The network diagram shows the time needed for each step in order to complete a project - HSC - SSCE Mathematics Standard - Question 3 - 2022 - Paper 1
Step 1
What is the critical path to complete the project?
Answer
To determine the critical path, we first need to identify all possible paths from the start to the end of the project based on the network diagram:
- Path ACI: A (3) → C (13) → I (2) = 3 + 13 + 2 = 18
- Path ADG: A (3) → D (16) → G (1) = 3 + 16 + 1 = 20
- Path BEH: B (2) → E (9) → H (6) = 2 + 9 + 6 = 17
- Path BEFG: B (2) → E (9) → F (2) → G (1) = 2 + 9 + 2 + 1 = 14
Next, we will summarize the total times for each path:
- ACI: 18
- ADG: 20
- BEH: 17
- BEFG: 14
The critical path is the one with the longest duration, which is ADG with a total time of 20.