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If the total float of an activity in CPM has a value ‘x’ units and the head event slack has a value ‘y’ units, find out the value of independent float if the tail event slack is 10. ?
- a)x-y-10
- b)x+y-2
- c)x-y+10
- d)x+y+2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the total float of an activity in CPM has a value ‘x’ units and th...
Reason: Free float = Total float – Head event slack
Free float =x-y
We know that,
Free float = Independent float + Tail event slack
x-y = Independent float + 10
Then, Independent float = x-y-10
Most Upvoted Answer
If the total float of an activity in CPM has a value ‘x’ units and th...
To find the value of independent float, we need to understand the concepts of float and slack in CPM (Critical Path Method) and how they are related.
Float in CPM:
Float is a measure of the flexibility or slack in a project schedule. It represents the amount of time that an activity can be delayed without affecting the project's overall completion time. There are two types of float: total float and free float.
- Total Float: It is the total amount of time that an activity can be delayed without delaying the project's completion time. It is calculated as the difference between the late finish time and early finish time of an activity.
- Free Float: It is the amount of time that an activity can be delayed without delaying the early start time of any successor activity.
Slack in CPM:
Slack is a measure of the flexibility or slack in an event (either head event or tail event) in a project network. It represents the amount of time that an event can be delayed without delaying the project's overall completion time. There are two types of slack: head event slack and tail event slack.
- Head Event Slack: It is the amount of time that an event can be delayed without delaying the early start time of any activity that leads to that event.
- Tail Event Slack: It is the amount of time that an event can be delayed without delaying the late start time of any activity that follows that event.
Now, let's solve the given problem step by step:
Given:
Total float of an activity = x units
Head event slack = y units
Tail event slack = 10 units
We need to find the value of independent float.
- Step 1: Understanding the relationship between float and slack:
Total float = Head event slack + Tail event slack
- Step 2: Substituting the given values:
x = y + 10
- Step 3: Solving the equation for y:
y = x - 10
- Step 4: Finding the value of independent float:
Independent float = Total float - Head event slack
Independent float = x - y
Independent float = x - (x - 10)
Independent float = x - x + 10
Independent float = 10
Therefore, the value of independent float is 10 units.
Float in CPM:
Float is a measure of the flexibility or slack in a project schedule. It represents the amount of time that an activity can be delayed without affecting the project's overall completion time. There are two types of float: total float and free float.
- Total Float: It is the total amount of time that an activity can be delayed without delaying the project's completion time. It is calculated as the difference between the late finish time and early finish time of an activity.
- Free Float: It is the amount of time that an activity can be delayed without delaying the early start time of any successor activity.
Slack in CPM:
Slack is a measure of the flexibility or slack in an event (either head event or tail event) in a project network. It represents the amount of time that an event can be delayed without delaying the project's overall completion time. There are two types of slack: head event slack and tail event slack.
- Head Event Slack: It is the amount of time that an event can be delayed without delaying the early start time of any activity that leads to that event.
- Tail Event Slack: It is the amount of time that an event can be delayed without delaying the late start time of any activity that follows that event.
Now, let's solve the given problem step by step:
Given:
Total float of an activity = x units
Head event slack = y units
Tail event slack = 10 units
We need to find the value of independent float.
- Step 1: Understanding the relationship between float and slack:
Total float = Head event slack + Tail event slack
- Step 2: Substituting the given values:
x = y + 10
- Step 3: Solving the equation for y:
y = x - 10
- Step 4: Finding the value of independent float:
Independent float = Total float - Head event slack
Independent float = x - y
Independent float = x - (x - 10)
Independent float = x - x + 10
Independent float = 10
Therefore, the value of independent float is 10 units.
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