Activity D on a CPM network has predecessors B and C, and has successor F. D has a duration of 6. B’s earliest finish is 18, while C’s is 20. F’s late start is 26. Which of the following is definitely true?- A. D is critical, and has a slack of two days.- B. B is a critical activity.- C. C is completed before B.- D. F is critical, and has zero slack.- E. D has no slack but is not critical.**Selected Answer**: A. D is critical, and has a slack of two days.

Earliest Start Time (ES) = Activity cannot be started before this day/weekEarliest Finish Time (EF) = Activity cannot be finished before this day/weekLate Start Time (LS) = activity cannot be completed after this , without delaying the projectLate Finish Time (LF) = activity cannot be started after this , without delaying the projectGiven:We know that D has predecessors B and C .D has 1 successor- F.We assume that there are no other successors / predecessors for B,C,F other than those given we assume Early start of project = day 0Early Finish of the activity,B=18Early Finish of the activity,C=20Late Start of Activity.F =26Activity duration D=6 Forward pass is a technique to move forward through network diagram . it helps use to find· the project duration · Early Start / Early Finish of the activity Early Start of the activity = Early Finish of predecessor activity Early Finish of the activity = Early Start of activity+ Activity duration Early start of first activity in a path is 0 , since it is started on day 0. If an activity has multiple predecessors, we chose the one with greater (latest)early finish date FORM Left TO LEFT:Early Start of the activity,D=max( Early Finish of predecessor activities)= max(18,20)=20 Early Finish of the activity,D = Activity duration + Early Start of activity= 20+6=26Early Start of the activity,F = Early Finish of predecessor activity D=26formulas:solution: A backward pass is a technique used to move through a project network diagram. It helps to identify your late start and late finish values.Late Finish of Activity = Late Start of successor activityIf an activity has multiple successors, we choose the one with (earliest) Late Start - least/smaller numberLate Start of Activity = Late Finish of activity – activity duration From RIGHT TO LEFT:Late Finish of Activity,D = Late Start of successor activity , F =26Late Start of Activity,D = Late Finish of activity – activity duration=26-6=20Late Finish of Activity,B = Late Start of successor activity = Late Start of A =20Late Finish of Activity,C= Late Start of successor activity == Late Start of A =20SLACK/FLOAT-(TF/SL)Slack is the amount of time that a task can be delayed without increasing the duration of the project. Float is sometimes referred to as slack. This is also called Total float,TF = LF-EF or LS-ES Critical activities have no slack. non-critical actIvities have slacks SLACK, B= LF-EF =20-18=2SLACK, c= LF-EF =20-20=0SLACK, d= LF-EF=26-26=0SLACK, f= LS-ES=26(given) - 26=0 D has no slack and is a critical activity. So it must be in a critical path. So, options A and E are ruled out. B has slack .Hence It is not a Critical activity. Option B is ruled out B cannot be completed after LF= 20.It can be completed on 18,19,20C cannot be completed before EF= 20.So ,C cannot completed before B.option C is ruled out F is critical and has zero slack. Option D is correct F is critical and has zero slack. Option D is correct