Critical Path Method (CPM)

Correct Answer: Critical path duration will increase by 3 days

The critical path is the sequence of activities that determine the minimum time required to complete the project. In this case, the critical path is L-M-N, with a total duration of 2 + 5 + 4 = 11 days. If activity L is extended by 3 days, its duration becomes 5 days. This directly impacts the critical path, as L is part of it. The new critical path duration will be 5 + 5 + 4 = 14 days. Therefore, the critical path duration will increase by 3 days, from 11 to 14 days. The other answers are incorrect because: - 'There will be no change in the critical path duration' is false, as the extension of activity L directly affects the critical path. - 'Critical path duration will decrease by 3 days' is false, as extending an activity on the critical path will increase, not decrease, the overall duration. - 'Critical path duration will increase by 2 days' is false, as the increase is equal to the extension of activity L, which is 3 days, not 2 days.

Correct Answer: The activity's position relative to parallel paths

The key factor in determining whether an activity's float can contribute to project acceleration is its position relative to parallel paths in the CPM network. This is the correct answer because: When activities are on parallel paths, their float relationships directly affect the potential for schedule compression. An activity's position in relation to other parallel paths determines if its float can be used to accelerate the project. Rationale for other options being incorrect: Duration compared to total slack is not the determining factor - it's the relationship between paths that matters. The total slack alone doesn't determine acceleration potential. While resource allocation and dependencies are important, they are secondary to the network path relationships in determining float contribution. Resource constraints, while relevant to scheduling, do not primarily determine how float can contribute to acceleration - the network structure and parallel paths are more fundamental.

Correct Answer: The difference between early finish and early start of successive tasks

The optimal float value in CPM for finish-to-start relationships between parallel activities is calculated as the difference between early finish and early start of successive tasks. This is correct because: - It measures the actual time buffer between dependent activities - It accounts for the sequential nature of finish-to-start relationships - It provides the true available float between connected activities The other options are incorrect because: - The sum of all possible delays would overstate the available float - Duration variance multiplied by resource utilization is not a CPM calculation method - Averaging slack time across parallel paths does not reflect true float relationships CPM float calculations must consider the specific timing relationships between activities, and the early finish to early start difference provides the most accurate measure of available float in finish-to-start dependencies.