# Given the following information about a small project, Task Duration Immediate Estimates Predecessors A 2 days None B 5 days A C 1 day B D 2 days A E 3 days B & D F 12 days E & C Draw a network diagram. Identify the critical path, earliest start and finish and slack for each task. Using MS Excel, produce a Gantt chart for this project. What would happen if a new estimate for task D increases its expected duration from two days to six days? Would the project take longer? Would anything else change?

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Computation of earliest starting and finishing times is aided by two simple rules:
1. The earliest finish time for any activity is equal to its earliest start time plus its expected
duration, t:
EF = ES + t
2. ES for activities at nodes with one entering arrow is equal to EF of the entering arrow. ES
for activities leaving nodes with multiple entering arrows is equal to the largest EF of the
entering arrow.
Computation of the latest starting and finishing times is aided by the use of two rules:
1. The latest starting time for each activity is equal to its latest finishing time minus its
expected duration:
LS = LF – t
2. For nodes with one leaving arrow, LF for arrows entering that node equals the LS of the
leaving arrow. For nodes with multiple leaving arrows, LF for arrows entering that node
equals the smallest LS of leaving arrows.
Finding ES and EF times involves a forward pass through the network; finding LS and LF
times involves a backward pass through the network. Hence, we must begin with the EF of the
last activity and use that time as the LF for the last activity. Then we obtain the LS for the last
activity by subtracting its expected duration from its LF
Slack = LS-ES = LF-EF
Activities for which Slack = 0 are in critical path
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If the activity time of D is changed from 2 to 6 days, there will be change in critical path as the slack time is 3 days and increase is by 4 days. The project will take longer time by 1 day to 23 days. So, both critical path and project duration will change

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