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Table 12-4
The following represents a project with known activity times. All times are in weeks.
Activity
Immediate
Predecessor
Time
A
--
4
B
--
3
C
A
2
D
B
7
E
C, D
4
F
B
5
G
E, F
4
82) Using the data in Table 12-4, what is the minimum possible time required for completing the project?
A) 8
B) 12
C) 18
D) 10
E) None of the above
83) Using the data in Table 12-4, what is the latest possible time that C may be started without delaying
completion of the project?
A) 0
B) 4
C) 8
D) 10
E) None of the above
84) Using the data in Table 12-4, compute the slack time for activity D.
A) 0
B) 5
C) 3
D) 6
E) None of the above
85) Using the data in Table 12-4, compute the latest finish time for activity E.
A) 4
B) 10
C) 14
D) 25
E) None of the above
86) Using the data in Table 12-4, determine the latest time activity A can be started without delaying the project
completion.
A) 4
B) 3
C) 8
D) 6
E) None of the above
87) Using the data in Table 12-4, determine the latest time activity A can be finished and not delay any activity?
A) 4
B) 0
C) 8
D) 5
E) None of the above
88) Consider a project that has an expected completion time of 50 weeks and a standard deviation of 9 weeks.
What is the probability that the project is finished in 57 weeks or fewer? (Round to two decimals.)
A) 0.68
B) 0.78
C) 0.22
D) 0.32
E) None of the above
89) Your company is considering submitting a bid on a major project. You determine that the expected
completion time is 150 weeks and the standard deviation is 10 weeks. It is assumed that the normal distribution
applies. You wish to set the due date for the project such that there is a 95 percent chance that the project will be
finished by this time. What due date should be set?
A) 108.0
B) 160.4
C) 166.5
D) 135.0
E) None of the above
Table 12-5
Activity
Immediate
Predecessor
Time
ES
EF
LS
LF
A
--
4
0
4
6
10
B
--
5
0
5
0
5
C
A
3
4
7
10
13
D
B
8
5
13
5
13
E
B
2
5
7
16
18
F
C, D
3
13
16
15
18
G
C, D
7
13
20
13
20
H
E, F
2
16
18
18
20
90) How long could Table 12-5's activity E be delayed without delaying the completion of the project?
A) 7
B) 16
C) 11
D) 18
E) None of the above
91) How long could Table 12-5's activity F be delayed without delaying the project?
A) 2
B) 3
C) 14
D) 16
E) None of the above
92) What is the minimum possible time required for completing the Table 12-5 project?
A) 14
B) 18
C) 17
D) 20
E) None of the above
Table 12-6
Activity
Immediate
Predecessor
Optimistic
Most
Likely
Pessimistic
σ
σ2
A
--
2
3
4
0.333
0.111
B
--
2
5
8
1.000
1.000
C
A
1
2
9
1.330
1.780
D
A
5
5
5
0.000
0.000
E
B, C
6
7
8
0.333
0.111
F
B
14
14
14
0.000
0.000
G
D, E
1
5
9
1.333
1.780
H
G, F
1
4
8
1.167
1.362
93) Which activities are part of Table 12-6's critical path?
A) A-B-E-G-H
B) A-C-E-G-H
C) A-D-G-H
D) B-F-H
E) None of the above
94) What is the variance of Table 12-6's critical path?
A) 5.222
B) 4.364
C) 1.362
D) 5.144
E) 2.362
Figure 12-1
95) Given the network in Figure 12-1, the critical path is
A) A-C-F-H.
B) B-D-E-F-H.
C) A-C-E-G-H.
D) B-D-G-E-F-H.
E) None of the above
96) Given the network in Figure 12-1, the time to complete those activities on the critical path is expected to be
________.
A) 20
B) 22
C) 25
D) 26
E) None of the above
97) Given the network shown in Figure 12-1, assume that completion of A is delayed by two days. What other
activities are impacted?
A) B
B) D
C) E
D) C
E) None of the above
98) Given the network shown in Figure 12-1, assume that completion of B is delayed by two days. What happens
to the project?
A) The critical path is extended by two days.
B) The start of activity F is delayed by two days.
C) The start of activity E is delayed by two days.
D) All of the above
E) None of the above
99) Given the network shown in Figure 12-1, assume that the completion of activity C is delayed by four days.
What changes will take place?
A) The critical path will change to: A-C-B-D-E-F-H.
B) Activity F will be delayed by four days.
C) Activity E will be delayed by four days.
D) Activity G will be delayed by four days.
E) None of the above
100) Given the network shown in Figure 12-1 and the following information, what is the variance of the critical
path?
Activity
Expected time
Variance
A
3
2
B
5
3
C
6
3
D
4
1
E
5
1
F
4
2
G
6
2
H
7
2
A) 16
B) 7
C) 9
D) 8
E) None of the above
101) PERT often assumes that time estimates follow which of the following probability distributions?
A) normal
B) exponential
C) binomial
D) Poisson
E) None of the above
102) PERT assumes that the total completion time of a projects follows which of the following probability
distributions?
A) normal
B) exponential
C) binomial
D) Poisson
E) None of the above
103) The crash time of an activity represents
A) the normal time to complete an activity.
B) the most pessimistic time to complete an activity.
C) the incremental decrease in the time to complete an activity.
D) the shortened activity time.
E) None of the above
104) Reducing the overall activity time is based on which of the following steps?
A) crashing activities with the lowest overall crash cost
B) crashing activities with the lowest overall normal cost
C) crashing activities on the critical path based on lowest overall cost
D) crashing activities on the critical path based on lowest cost/week
E) crashing activities with the lowest cost/week.
105) An alternative approach to project crashing is to use which of the following techniques?
A) linear programming
B) nonlinear programming
C) Markov analysis
D) queuing theory
E) None of the above
106) Which of the following is not a decision variable when formulating the project crashing problem as a linear
program?
A) the early finish times of critical activities
B) the early finish times of non critical activities
C) the start time of the project
D) the finish time of the project
E) the early start times of all activities
107) Which of the following statement about project crashing is false?
A) The crash cost is greater than or equal to the normal cost of an activity.
B) The crash time is less than or equal to the normal time to complete an activity.
C) Reducing the time of an activity on the critical path automatically reduces total project duration.
D) It may not be possible to crash a particular activity.
E) Crashing may not lead to an overall reduction in costs for the project.
108) The process of smoothing out the utilization of resources in a project is called
A) CPM.
B) PERT.
C) project crashing.
D) work breakdown structure.
E) resource leveling.
109) Consider the following project schedule:
Activity
Immediate
Predecessor
Time
ES
EF
LS
LF
A
--
4
0
4
6
10
B
--
5
0
5
0
5
C
A
3
4
7
10
13
D
B
8
5
13
5
13
E
B
2
5
7
16
18
F
C, D
3
13
16
15
18
G
C, D
7
13
20
13
20
H
E, F
2
16
18
18
20
(a) Which activities are critical?
(b) Which activity has the most slack?
110) Consider the project with the following estimates for activity times and precedence relationships:
Activity
Optimistic
Time
Most
Likely Time
Pessimistic
Time
Immediate
Predecessor(s)
A
3
4
5
---
B
5
7
9
---
C
2
3
10
A
D
2
5
8
B
E
1
7
7
B
F
3
5
7
C, D
G
7
8
9
D, E
H
2
6
10
F
(a) What is the expected duration of the project?
(b) What is the project variance?
(c) If the deadline of the project is 25 days, what is the probability of finishing the project on time?
111) Consider the tasks, durations, and predecessor relationships in the following network. Draw the network
and answer the questions that follow.
Activity
Immediate
Predecessors)
Optimistic
(Weeks)
Most Likely
(Weeks)
Pessimistic
(Weeks)
A
---
4
7
10
B
A
2
8
20
C
A
8
12
16
D
B
1
2
3
E
D, C
6
8
22
F
C
2
3
4
G
F
2
2
2
H
F
6
8
10
I
E, G, H
4
8
12
J
I
1
2
3
(a) What is the expected duration of the project?
(b) What is the probability of completion of the project before week 42?
112) Given:
Activity
Optimistic
Most
Likely
Pessimistic
A
3
4
5
B
6
7
14
C
6
9
12
D
0.5
1
1.5
E
2
3
10
F
4
5
12
G
1
3
11
Determine:
(a) the critical path.
(b) the probability that the project will be completed in 22 weeks.
113) A small software development project has five major activities. The times are estimated and provided in the
table below.
Activity
Immediate
Predecessor
a
m
b
A
--
2
5
8
B
--
10
10
10
C
A
4
7
10
D
B
2
5
14
E
C
3
3
3
(a) What is the expected completion time for this project?
(b) What variance would be used in finding probabilities of finishing by a certain time?
114) Development of a new deluxe version of a particular software product is being considered. The activities
necessary for the completion of this are listed in the table below (Time in weeks).
Activity
Normal
Time
Crash
Time
Normal
Cost
Crash
Cost
Immediate
Predecessor
A
4
3
2200
2600
--
B
2
1
2200
2800
--
C
3
3
500
500
--
D
8
4
2300
2600
A
E
6
3
900
1200
B
F
3
2
3000
4200
C
G
4
2
1400
2000
D, E
(a) What is the project completion date?
(b) What is the total cost required for completing this project on normal time?
(c) If you wish to reduce the time required to complete this project by one week, which activity should be
crashed, and how much will this increase the total cost?
115) Draw the PERT network associated with the following activities.
Activity
Immediate
Predecessor
A
--
B
A
C
A
D
B
E
B
F
C, E
G
A, D
H
F
I
F
J
G, H, I
116) Given (Time in weeks):
Activity
Optimistic
Most Likely
Pessimistic
A
3
4
5
B
6
7
14
C
2
3
10
D
6
9
12
E
4
5
12
F
1
3
11
G
1
2
9
H
2
5
8
I
1
4
7
Determine:
(a) the critical path.
(b) the probability that the project will be completed in 22 weeks.
117) A small software development project has four major activities. The times are estimated and provided in the
table below.
Activity
Immediate
Predecessor
a
m
b
A
--
2
5
8
B
A
3
6
9
C
A
4
7
10
D
B
2
5
14
E
D
3
3
3
F
C
6
8
10
G
E, F
1
1
1
H
C
6
10
14
I
G, H
3
4
5
(a) What is the expected completion time for this project?
(b) What variance would be used in finding probabilities of finishing by a certain time?
118) Development of a new deluxe version of a particular software product is being considered. The activities
necessary for the completion of this are listed in the table below (Time in weeks).
Activity
Immediate
Predecessor
a
m
b
A
--
2
5
8
B
A
3
6
9
C
A
4
7
10
D
B
2
5
14
E
D
3
3
3
F
C
6
8
10
G
E, F
1
1
1
H
C
6
10
14
I
G, H
3
4
5
(a) If you wish to reduce the time required to complete this project by two weeks, which activity(ies) should
be crashed, and how much will this increase the total cost?
(b) What would be the added cost if you wanted to complete the project in the minimum time possible?
119) PERT is the acronym for what?
120) In a PERT analysis, how is the optimistic time defined?
121) CPM is the acronym for what?
122) In PERT analysis, how is the pessimistic activity time defined?
123) In PERT/CPM, what is meant by the critical path?
