Slack and Float MCQ Quiz in मराठी - Objective Question with Answer for Slack and Float - मोफत PDF डाउनलोड करा
Last updated on Mar 26, 2025
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Slack and Float Question 1:
The free float for activity (4 - 5) for the network shown below is ______
Answer (Detailed Solution Below) 0
Slack and Float Question 1 Detailed Solution
Explanation:
Path 1 – 3 – 4 – 6 – 7 shows critical path.
Δ ⇒ represents Earliest occurrence time of event.
□ ⇒ represents latest occurrence time of event.
Now,
For activity 4 – 5,
Total float = Lj – (Ei + tij)
Where, tij is duration of activity,
Now,
Total float = 57 – (39 + 0)
∴ Total float = 18
Free float = Total float – Head event slack
∴ Free float = 18 – (57 - 39)
∴ Free float = 0
Slack and Float Question 2:
Consider the given project network, where sum of numbers along various activities represent normal time. The sum of free float on activity 3-6 and activity 4-6 is ______
Answer (Detailed Solution Below) 3
Slack and Float Question 2 Detailed Solution
Now, finding the Ei and Li details for the network given.
The critical path is 1-2-5-6-7
Now, Free float for activity (i - j) = Ej – (Ei + tEij)
For Activity 3 – 6, FF = 8 – (2 + 5) = 1
For activity 4 – 6, FF = 8 – (2 + 4) = 2
∴ Total free float on activity 3 – 6 and 4 – 6 = 1 + 2 = 3
Slack and Float Question 3:
The variable that is included in the ‘≤’ type inequality constraint for the purpose of converting general form of LPP to standard form of LPP is called:
Answer (Detailed Solution Below)
Slack and Float Question 3 Detailed Solution
Explanation
Steps involved in solving LPP problems.
- Write the given LPP problem in normal form, in a form in which all constraints are written as equations.
- To write the problem in normal form, first, transform all constraints, so that right-hand side values are non-negative.
- Add or Subtract additional variables to and from left-hand sides of the given constraints.
|
Types of constraints (Relation R) |
Additional Variables(s) |
Constraint |
|
≤ |
Slack variable S |
LHS + S = RHS |
|
≥ |
Excess (or surplus) E and artificial variable A |
LHS – E + A = RHS |
|
= |
Artificial variable A |
LHS + A = RHs |
Slack and Float Question 4:
For the critical path network shown, the slack for the activity ‘b’ in months, is
|
Activity |
Duration (Months) |
|
a |
4 |
|
b |
3 |
|
c |
5 |
|
d |
4 |
|
e |
7 |
Answer (Detailed Solution Below)
Slack and Float Question 4 Detailed Solution
Now,
Slack and Float Question 5:
A small project is compared of 7 activities whose network is given below with three times indicated on arrows.
Calculate the difference in free floats for activities 4 – 6 & 2 – 5.
Answer (Detailed Solution Below)
Slack and Float Question 5 Detailed Solution
First calculated expected time for each activity.
|
Activity (i – j) |
Times |
Expected time |
||
|
|
to |
tm |
tp |
|
|
1 – 2 |
1 |
1 |
7 |
2 |
|
1 – 3 |
1 |
4 |
7 |
4 |
|
1 – 4 |
2 |
2 |
8 |
3 |
|
2 – 5 |
1 |
1 |
1 |
1 |
|
3 – 5 |
2 |
5 |
14 |
6 |
|
4 – 6 |
2 |
5 |
8 |
5 |
|
5 - 6 |
3 |
6 |
15 |
7 |
Free float (Ff)ij = Ej - Ei - Dij
(FF)4-6 = 17– 3 – 5 = 9
(FF)2-5 = 10 – 2 – 1 = 7
Required difference = (FF)4-6 – (FF)2-5
= 9 – 7
= 2Slack and Float Question 6:
In PERT/CPM chart, slack of various events on the critical path
Answer (Detailed Solution Below)
Slack and Float Question 6 Detailed Solution
Slack and Float Question 7:
The amount of time by which an activity can be delayed without affecting project completion time is
Answer (Detailed Solution Below)
Slack and Float Question 7 Detailed Solution
Explanation
Slack or Event Float
- Slack corresponds to the event in PERT.
- Float corresponds to activity in CPM.
Slack
- It is defined as the amount of time by which an event can be delayed without delaying the project schedule.
- Slack of an event = Latest Start Time – Earliest Start Time OR Latest Finish Time – Earliest Finish Time
There are three types of floats.
|
Total Float (TF) |
|
|
Free Float (FF) |
· Part of the Total Float, which can be used without affecting the float of succeeding activity. · Extra time by which an activity can be delayed so that the succeeding activity can be started on earliest start time.
|
|
Independent Float (IF) |
|
Slack and Float Question 8:
For the given network of a project,
Answer (Detailed Solution Below)
Slack and Float Question 8 Detailed Solution
Concept:
Float:
- Relax or delay provided to any activity is known as float.
Floats are of three types. They are as follows:
Total Float (TF):
The maximum delay or relax provided to any activity without affecting the project duration.
TF = Lj - Ei - dij
Free Float (FF):
Relax or delay provided to any activity without affecting the Earliest Start Time (EST) of the successor activity.
FF = Ej - Ei - dij
Independent Float:
Relax or delay provided to any activity without affecting the Earliest Start Time (EST) of successor activity as well as Latest Finish Time (LFT) of the predecessor activity.
IF = Ej - Li - dij
Relation among float TF ≥ FF ≥ IF
On the Critical path, total, free, and independent float are all equal and zero.
Calculation:
Now the network diagram with occurrence times is
Δ ⇒ represents Earliest occurrence time of event.
□ ⇒ represents latest occurrence time of event.
For activity 3 - 4:
The total float will be
TF = Lj - Ei - dij = 39 - 23 - 16 = 0;
The free float will be
FF = Ej - Ei - dij = 39 - 23 - 16 = 0;
For activity 5 - 6:
The total float will be
TF = Lj - Ei - dij = 57 - 57 - 0 = 10
The free float will be
FF = Ej - Ei - dij = 39 - 39 - 0 = 0
Slack and Float Question 9:
For the given network, what is the value of total float for activity P?
Answer (Detailed Solution Below) 2
Slack and Float Question 9 Detailed Solution
Concept:
Total float is the maximum amount of time an activity can be delayed without delaying the project:
TF = LF – EF
OR, TF = LS – ES
LS, ES ⇒ Earliest and latest (LS) start
LF, EF ⇒ Latest finish, Earliest finish.
Calculation:
|
Activity |
Time (Duration) |
Earliest Time |
Latest time |
Total float (Lj - Ei) - dij |
||
|
|
|
Ei |
Ei + dij |
ly - dij |
Lj |
|
|
1 – 2 |
4 |
0 |
4 |
3 |
7 |
3 |
|
1 – 3 |
7 |
0 |
7 |
0 |
7 |
0 |
|
1 – 4 |
6 |
0 |
6 |
8 |
14 |
8 |
|
→ 3 – 4 |
5 |
7 |
12 |
9 |
14 |
|
|
3 – 5 |
7 |
7 |
14 |
9 |
14 |
0 |
|
5 – 7 |
6 |
14 |
20 |
14 |
20 |
0 |
|
5 - 6 |
5 |
14 |
19 |
15 |
20 |
1 |
Slack and Float Question 10:
If earliest starting time of an activity is 8 weeks, the latest finish time is 37 weeks and the duration time of the activity is 11 weeks, the total float is ________ weeks
Answer (Detailed Solution Below) 18
Slack and Float Question 10 Detailed Solution
Concept:
For an activity,
d = duration of activity
Es = Earliest start of activity
EF = Earliest finish of activity
Ls = Latest start of activity
Lf = Latest finish of activity
Total float = Lf - Es – d
Calculation:
∴ Total float = 37 – 8 – 11 = 18