Consider the following project consisting of activities given in the table. For the activity durations, optimistic, pessimistic and most likely estimates are on hand. Draw the AON network and answer the following questions. | Time (days) | | m| b| Predecessor Activity a A 3 6. 8. В 4 4 1 3 D E B,D F 6. 10 14 A,E 1 4 A,E H 3. 6. 9. I 10 11 12 G J 14 16 20 к 2 H,I 10 (a) Compute the expected completion time and the variance of the project (b) Find the critical path (c) Determine ES, EF, LS, LF, and slack for each activity (d) What is the probability that the project is finished in 40 days or less.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Question
Consider the following project consisting of activities given in the table. For the activity
durations, optimistic, pessimistic and most likely estimates are on hand. Draw the AON network and
answer the following questions.
| Time (days)
|m b Predecessor
Activity
a
A
3
6.
в
2
4
4
2
3
D
6.
7
E
4
6.
B,D
10
14
A,E
G
1
2
4
A,E
H
3
F
10
11
12
G
J
14
16
20
K
2
8
10
H,I
(a) Compute the expected completion time and the variance of the project
(b) Find the critical path
(c) Determine ES, EF, LS, LF, and slack for each activity
(d) What is the probability that the project is finished in 40 days or less.
Transcribed Image Text:Consider the following project consisting of activities given in the table. For the activity durations, optimistic, pessimistic and most likely estimates are on hand. Draw the AON network and answer the following questions. | Time (days) |m b Predecessor Activity a A 3 6. в 2 4 4 2 3 D 6. 7 E 4 6. B,D 10 14 A,E G 1 2 4 A,E H 3 F 10 11 12 G J 14 16 20 K 2 8 10 H,I (a) Compute the expected completion time and the variance of the project (b) Find the critical path (c) Determine ES, EF, LS, LF, and slack for each activity (d) What is the probability that the project is finished in 40 days or less.
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
.0
.5000
.5040
.5080
.5120
.5160
.5199
.5239
.5279
.5319
.5359
.1
.5398
.5438
5478
.5517
5557
.5596
.5636
.5675
.5714
.5753
.2
.5793
.5832 5871 .5910
.5948
.5987
.6026
.6064
.6103
.6141
.3
.6179
.6217 6255
.6293
.6331
.6368
.6406
.6443
.6480
.6517
.4
.6554 .6591
.6628
.6664
.6700
.6736
.6772
.6808
.6844
.6879
.5
.6915
.6950
.6985
.7019
.7054
.7088
.7123
.7157
.7190
.7224
.6
.7257
.7291
.7324
.7357
.7389
.7422
.7454
.7486
.7517
.7549
.7
.7580
.7611
.7642
.7673
.7704
.7734
.7764
.7794
.7823
.7852
.8
.7881
.7910
.7939
.7967
.7995
.8023
.8051
.8078
8106
.8133
.9
.8159
.8186
.8212
.8238
.8264
.8289
.8315
.8340
.8365
.8389
1.0
.8413
.8438
.8461
.8485
.8508
.8531
.8554
.8577
.8599
.8621
1.1
.8643
.8665
.8686
.8708
.8729
.8749
.8770
.8790
.8810
.8830
1.2
.8849
.8869
.8888
.8907
.8925
.8944
.8962
.8980
.8997
.9015
1.3
.9032
.9049
.9066
.9082
.9099
.9115
9131
.9147
.9162
.9177
1.4
.9192
.9207
.9222
.9236 9251
.9265
.9279
9292
.9306
.9319
1.5
.9332
.9345
.9357
.9370 9382
.9484
.9394
9406
.9418
.9429
.9441
.9452
.9554
.9463
.9564
1.6
9474
.9495
.9505
.9515
.9525
.9535
.9545
.9633
.9706
1.7
.9573
.9582
9591
.9599
9608
.9616
9625
1.8
.9641
9649
9656
.9664
9671
.9678
.9686
.9693
.9699
1.9
.9713
.9719
9726
.9732
.9738
.9744
.9750
.9756
.9761
.9767
2.0
.9772
.9778
9783
.9788 9793
.9798
.9803
9808
.9812
.9817
2.1
.9821
2.2 9861
.9826
.9830
.9834
.9838
.9842
.9846
.9850
.9854
.9857
.9864
.9868
9871
9875
.9878
9881
.9884
.9887
.9890
2.3
.9893
.9896
9898
.9901
.9904
9906
.9909
.9911
.9913
.9916
2.4
.9918
9920
.9922
.9925
.9927
.9929
.9931
.9932
.9934
.9936
.9941
.9943
9956 9957
9951
.9946
.9960
2.5
.9938 9940
.9945
.9948
.9949
.9952
2.6
.9953
.9955
.9959
.9961 .9962 9963
.9964
2.7
2.8
.9965
.9974 9975 9976 .9977 9977 9978
.9966
9967 9968
9969
9970 9971 9972 9973
.9974
.9979
.9979 9980
.9981
2.9
.9981
.9982
9982
.9983
.9984
.9984
.9985
.9985
.9986
.9986
3.0
.9987 9987 9987 9988 9988
9989
.9989
.9989
.9990
.9990
Figure 1: Z table
Transcribed Image Text:.00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .0 .5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359 .1 .5398 .5438 5478 .5517 5557 .5596 .5636 .5675 .5714 .5753 .2 .5793 .5832 5871 .5910 .5948 .5987 .6026 .6064 .6103 .6141 .3 .6179 .6217 6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517 .4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879 .5 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7224 .6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549 .7 .7580 .7611 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .7852 .8 .7881 .7910 .7939 .7967 .7995 .8023 .8051 .8078 8106 .8133 .9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389 1.0 .8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .8621 1.1 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830 1.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .9015 1.3 .9032 .9049 .9066 .9082 .9099 .9115 9131 .9147 .9162 .9177 1.4 .9192 .9207 .9222 .9236 9251 .9265 .9279 9292 .9306 .9319 1.5 .9332 .9345 .9357 .9370 9382 .9484 .9394 9406 .9418 .9429 .9441 .9452 .9554 .9463 .9564 1.6 9474 .9495 .9505 .9515 .9525 .9535 .9545 .9633 .9706 1.7 .9573 .9582 9591 .9599 9608 .9616 9625 1.8 .9641 9649 9656 .9664 9671 .9678 .9686 .9693 .9699 1.9 .9713 .9719 9726 .9732 .9738 .9744 .9750 .9756 .9761 .9767 2.0 .9772 .9778 9783 .9788 9793 .9798 .9803 9808 .9812 .9817 2.1 .9821 2.2 9861 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9857 .9864 .9868 9871 9875 .9878 9881 .9884 .9887 .9890 2.3 .9893 .9896 9898 .9901 .9904 9906 .9909 .9911 .9913 .9916 2.4 .9918 9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936 .9941 .9943 9956 9957 9951 .9946 .9960 2.5 .9938 9940 .9945 .9948 .9949 .9952 2.6 .9953 .9955 .9959 .9961 .9962 9963 .9964 2.7 2.8 .9965 .9974 9975 9976 .9977 9977 9978 .9966 9967 9968 9969 9970 9971 9972 9973 .9974 .9979 .9979 9980 .9981 2.9 .9981 .9982 9982 .9983 .9984 .9984 .9985 .9985 .9986 .9986 3.0 .9987 9987 9987 9988 9988 9989 .9989 .9989 .9990 .9990 Figure 1: Z table
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