QuestionRefer to the project described by the project digraph shown on the right Complete parts (a) and (b) below. (a) Find the critical path for the project. Choose the correct answer below. A. START, B, E, I, K, END B. START, C, G, K, END C. START, B, F, I, K, END D. START, A, E, I, K, END
Studdy Solution
STEP 1
1. The project digraph represents tasks and their durations.
2. The critical path is the longest path through the network, determining the shortest time to complete the project.
3. Each node represents a task, and the number in parentheses is the duration of that task.
4. Arrows indicate the sequence of tasks.
STEP 2
1. Identify all possible paths from START to END.
2. Calculate the total duration for each path.
3. Determine the path with the longest duration (critical path).
STEP 3
Identify all possible paths from START to END by following the arrows in the digraph.
Possible paths:
- START, A, E, I, K, END
- START, B, E, I, K, END
- START, B, F, I, K, END
- START, C, G, K, END
STEP 4
Calculate the total duration for each identified path by summing the durations of the tasks in each path.
- Path 1: START, A, E, I, K, END
$ \text{Duration} = 9 + 9 + 8 + 9 = 35
\]
- Path 2: START, B, E, I, K, END
$ \text{Duration} = 11 + 9 + 8 + 9 = 37
\]
- Path 3: START, B, F, I, K, END
$ \text{Duration} = 11 + 6 + 8 + 9 = 34
\]
- Path 4: START, C, G, K, END
$ \text{Duration} = 10 + 5 + 9 = 24
\]
STEP 5
Determine the path with the longest duration. This path is the critical path.
The longest duration is 37, which corresponds to the path:
- START, B, E, I, K, END
The critical path for the project is:
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