Answer:
Step-by-step explanation:
To determine the maximum number of projects that can be finished in 60 working days, we need to consider the dependencies and duration of each activity.
Let's analyze the given activities and their duration:
A (5 days) --> B (15 days) --> C (10 days)
Based on the dependencies, activity B cannot start until activity A is completed, and activity C cannot start until activity B is completed.
To maximize the number of projects, we need to identify the critical path, which is the longest path that determines the total project duration.
In this case, the critical path is A --> B --> C, with a total duration of 5 + 15 + 10 = 30 days.
Since the critical path takes 30 days, we can complete a maximum of 60/30 = 2 projects within 60 working days.
Therefore, the maximum number of projects that can be finished in 60 working days, assuming no work has started on any project, is 2 projects.
To prove that the maximum number of projects that can be finished in 60 working days, assuming no work has started on any project, is 2 projects, we need to show that it is not possible to complete more than 2 projects within the given time frame.
Let's analyze the activities and their duration:
A (5 days) --> B (15 days) --> C (10 days)
Based on the dependencies, activity B cannot start until activity A is completed, and activity C cannot start until activity B is completed.
To complete one project, we need to finish all three activities: A, B, and C. The total duration for one project is 5 + 15 + 10 = 30 days.
If we start the first project on day 1, it will take 30 days to complete. Then, we can start the second project on day 31 and complete it in the next 30 days. Therefore, within 60 working days, we can complete a maximum of 2 projects.
To prove that it is not possible to complete more than 2 projects, let's consider the scenarios:
If we try to start a third project on day 61, it will not be possible to complete it within the 60 working days since the total duration of each project is 30 days.
If we try to overlap the projects and start the second project before completing the first one, we would still need a minimum of 30 days to complete each project. Thus, we can only complete a maximum of 2 projects within the given time frame.
Therefore, we have proven that the maximum number of projects that can be finished in 60 working days, assuming no work has started on any project, is 2 projects.