Answer:
a. The normal project length is 36 weeks.
b. The critical path in this project is A-C-E-F.
c. The activity that you choose to crash first to reduce the duration of the project by one week is E because it has the least expediting cost/week amongst A, C, E, F.
d. The project length if all activities are crashed to their minimum is 23 weeks.
e. The slack for activity D is 5 weeks.
Explanation:
a) The normal length of the project = completion time of last activity = 36 weeks.
b) The criteria for critical activity:
[tex]LC_{i} = ES_{i} ,\\LC_{j} = ES_{j} ,\\[/tex]
[tex]ES_j - ES_i = LF_j - LF_{i} =[/tex] duration of the activity
where ES = Earliest start time, EF = Earliest finish time , LC = latest completion time, LF = latest finish time ,
The suffix- i refers to the preceding node, suffix-j refers to the succeeding node.
activities satisfying above all criteria are A, C, E, F
therefore critical path is A-C-E-F.
c) To reduce the project duration by 1 week. we should choose to crash among critical activities A, C, E, F. thus we choose to crash activity E because it has the least expediting cost/week amongst A, C, E, F.
d) if we crash all the activities to their minimum, then the project length = sum of crash time of all critical activities
= [6 + 10 + 6 + 1]
= 23 weeks.
e) The slack of activity d = LS - ES = 34 - 29
= 5 weeks
The critical path is given in the diagram,
