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Problem 17-5 For each of the problems listed, determine the following quantities

ID: 453495 • Letter: P

Question

Problem 17-5

For each of the problems listed, determine the following quantities for each activity: the earliest start time, latest start time, earliest finish time, latest finish time, and slack time. List the critical activities, and determine the expected duration of the project.

   

a.

   

b.

    
c.

   

For each of the problems listed, determine the following quantities for each activity: the earliest start time, latest start time, earliest finish time, latest finish time, and slack time. List the critical activities, and determine the expected duration of the project.

Explanation / Answer

EARLIEST TIMES

ES is the earliest time an activity can start.

ESij = Maximum (EFi)

EF is the earliest start time plus the activity time.

EFij = ESij + tij

LATEST TIMES

LS is the latest time an activity can start.

LSij = LFij – tij

LF is the latest start time plus the activity time.

LFij = Minimum (LSj)

Slack = LS-ES or LF-EF

Critical path is the one on which activities have zero slack.

Expected duration is sum of the duration of critical path activities

Using all this information:

1)

Critical Path = 1-3-6-9-11-12

Duration of the project = 10+6+4+5+6 = 31

2)

Critical Path = 1-2-5-7-8-9

Duration of the project = 5+18+10+11+9+2 = 55

3)

Critical Path = F-H-J-K

Duration of the project = 8+9+14+6 = 37 days

Activity Activity time    ES          EF            LF           LS        Slack   1–2         4 0 4 10 6 6 2–4         9 4 13 19 10 6 4–7         5 13 18 24 19 6 7–10         2 18 20 26 24 6 10–12         3 21 24 31 28 7 2–5         8 4 12 19 11 7 5–8         7 12 19 26 19 7 8–10         2 19 21 28 26 7 1–3         10 0 10 10 0 0 3–6         6 10 16 16 10 0 6–9         4 16 20 20 16 0 9–11         5 20 25 25 20 0 11–12         6 25 31 31 25 0