The table below shows the activities, their immediate predecessors and activity time estimates (in hours) of a project. Immediate Most Activity Optimistic Pessimistic Predecessor Probable A 2.5 4 5.5 B 3 4.5 9. А, В 3 10 D B 5 13 E А, В 8 16 F C 5.5 10 G C, D, E 6. 7.5 12 (a) Determine the mean time and variance for each activity. (b) Construct a complete project network for the project. (c) Define the random variable T = completion time of the project. Find the mean and the standard deviation of T. 64

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The table below shows the activities, their immediate predecessors and activity time
estimates (in hours) of a project.
Immediate
Most
Activity
Optimistic
Pessimistic
Predecessor
Probable
A
2.5
4
5.5
В
3
4.5
9
C
А, В
3
10
D
B
6.
13
E
А, В
8
16
F
C
4
5.5
10
G
С, D, E
7.5
12
(а)
Determine the mean time and variance for each activity.
(b) Construct a complete project network for the project.
(c) Define the random variable T = completion time of the project. Find the mean and
the standard deviation of T.
(d) What is the probability that the project is completed in 19 hours? (You must use
the Normal Table provided in class.)
(e) Suppose the (mean) times of D, E, F and G can be reduced by 2 hours, 1 hour, 2
hours and 3 hours respectively, with crash costs of $80, $120, $110 and $95 per
hour respectively. Formulate a linear program to minimize the total crash cost if
the project is to be completed in 19 hours.
Transcribed Image Text:The table below shows the activities, their immediate predecessors and activity time estimates (in hours) of a project. Immediate Most Activity Optimistic Pessimistic Predecessor Probable A 2.5 4 5.5 В 3 4.5 9 C А, В 3 10 D B 6. 13 E А, В 8 16 F C 4 5.5 10 G С, D, E 7.5 12 (а) Determine the mean time and variance for each activity. (b) Construct a complete project network for the project. (c) Define the random variable T = completion time of the project. Find the mean and the standard deviation of T. (d) What is the probability that the project is completed in 19 hours? (You must use the Normal Table provided in class.) (e) Suppose the (mean) times of D, E, F and G can be reduced by 2 hours, 1 hour, 2 hours and 3 hours respectively, with crash costs of $80, $120, $110 and $95 per hour respectively. Formulate a linear program to minimize the total crash cost if the project is to be completed in 19 hours.
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