Mathematics Assignment-Quant. Analysis
1. The critical path of a network is the
A) shortest time path through the network.
B) path with the fewest activities.
C) path with the most activities.
D) longest time path through the network.
E) None of the above
2. The first step in planning and scheduling a project is to develop the
A) employee scheduling plan.
B) PERT/CPM network diagram.
C) critical path.
D) work breakdown structure.
E) variance calculations for each activity.
Table 13-4
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
3. Using the data in Table 13-4, what is the minimum possible time required for
completing the project?
(a) 8
(b) 12
(c) 18
(d) 10
(e) none of the above
4. Using the data in Table 13-4, 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
5. Using the data in Table 13-4, compute the slack time for activity D.
(a) 0
(b) 5
(c) 3
(d) 6
(e) none of the above
6. 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
The following table provides information for the next two questions.
Table 13-6
Activity
Immediate
Predecessor
Optimistic
Most
Likely
Pessimistic
Expec-ted t
s
s2
A
-
2
3
4
3
0.333
0.111
B
-
2
5
8
5
1.000
1.000
C
A
1
2
9
3
1.330
1.780
D
A
5
5
5
5
0.000
0.000
E
B, C
6
7
8
7
0.333
0.111
F
B
12
12
12
12
0.000
0.000
G
D, E
1
5
9
5
1.333
1.780
H
G, F
1
4
8
4.167
1.167
1.362
7. Which activities are part of the 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
8. What is the variance of the critical path?
(a) 5.222
(b) 4.364
(c) 1.362
(d) 5.144
(e) none of the above
Table 14-1
M/M/2
Mean Arrival Rate:
9 occurrences per minute
Mean Service Rate:
7 occurrences per minute
Number of Servers:
2
Queue Statistics:
Mean Number of Units in the System:
2.191
Mean Number of Units in the Queue:
0.905
Mean Time in the System:
14.609 minutes
Mean Time in the Queue:
6.037 minutes
Service Facility Utilization Factor:
0.643
Probability of No Units in System:
0.217
9. According to the information provided in Table 14-1, on average, how many units are
in the line?
(a) 0.643
(b) 2.191
(c) 2.307
(d) 0.217
(e) 0.905
10. According to the information provided in Table 14-1, what proportion of time is at
least one server busy?
(a) 0.643
(b) 0.905
(c) 0.783
(d) 0.091
(e) none of the above
11. Using the information provided in Table 14-1 and counting each person being served
and the people in line, on average, how many people would be in this system?
(a) 0.905
(b) 2.191
(c) 6.037
(d) 14.609
(e) none of the above
12. According to the information provided in Table 14-1, what is the average time spent
by a person in this system?
(a) 0.905 minutes
(b) 2.191 minutes
(c) 6.037 minutes
(d) 14.609 minutes
(e) none of the above
13. According to the information provided in Table 14-1, what percentage of the total
available service time is being used?
(a) 90.5%
(b) 21.7%
(c) 64.3%
(d) It could be any of the above, depending on other factors.
(e) none of the above
Table 14-5
M/D/1
Mean Arrival Rate:
5 occurrences per minute
Constant Service Rate:
7 occurrences per minute
Queue Statistics:
Mean Number of Units in the System:
1.607
Mean Number of Units in the Queue:
0.893
Mean Time in the System:
0.321 minutes
Mean Time in the Queue:
0.179 minutes
Service Facility Utilization Factor:
0.714
14. According to the information provided in Table 14-5, which presents the solution for
a queuing problem with a constant service rate, on average, how much time is spent
waiting in line?
(a) 1.607 minutes
(b) 0.714 minutes
(c) 0.179 minutes
(d) 0.893 minutes
(e) none of the above
15. According to the information provided in Table 14-5, which presents the solution for
a queuing problem with a constant service rate, on average, how many customers are
in the system?
(a) 0.893
(b) 0.714
(c) 1.607
(d) 0.375
(e) none of the above
16. According to the information provided in Table 14-5, which presents a queuing
problem solution for a queuing problem with a constant service rate, on average, how
many customers arrive per time period?
(a) 5
(b) 7
(c) 1.607
(d) 0.893
(e) none of the above
Table 15-2
A pharmacy is considering hiring another pharmacist to better serve customers. To help analyze this situation, records are kept to determine how many customers will arrive in any 10-minute interval. Based on 100 ten-minute intervals, the following probability distribution has been developed and random numbers assigned to each event.
Number of Arrivals
Probability
Interval of Random Numbers
6
0.2
01-20
7
0.3
21-50
8
0.3
51-80
9
0.1
81-90
10
0.1
91-00
17. According to Table 15-2, the number of arrivals in any 10-minute period is between 6
and 10, inclusive. Suppose the next three random numbers were 18, 89, and 67, and
these were used to simulate arrivals in the next three 10-minute intervals. How many
customers would have arrived during this 30-minute time period?
(a) 22
(b) 23
(c) 24
(d) 25
(e) none of the above
18. According to Table 15-2, the number of arrivals in any 10-minute period is between
6 and 10, inclusive. Suppose the next three random numbers were 20, 50, and 79, and
these were used to simulate arrivals in the next three 10-minute intervals. How many
customers would have arrived during this 30-minute time period?
(a) 18
(b) 19
(c) 20
(d) 21
(e) none of the above
19. According to Table 15-2, the number of arrivals in any 10-minute period is between 6
and 10 inclusive. Suppose the next 3 random numbers were 02, 81, and 18. These
numbers are used to simulate arrivals into the pharmacy. What would the average
number of arrivals per 10-minute period be based on this set of occurrences?
(a) 6
(b) 7
(c) 8
(d) 9
(e) none of the above
Table 15.3
A pawn shop in Arlington, Texas, has a drive-through window to better serve customers. The following tables provide information about the time between arrivals and the service times required at the window on a particularly busy day of the week. All times are in minutes.
Time Between Arrivals
Probability
Interval of Random Numbers
1
0.1
01-10
2
0.3
11-40
3
0.4
41-80
4
0.2
81-00
Service Time
Probability
Interval of Random Numbers
1
0.2
01-20
2
0.4
21-60
3
0.3
61-90
4
0.1
91-00
The first random number generated for arrivals is used to tell when the first customer arrives after opening.
20. According to Table 15-3, the time between successive arrivals is 1, 2, 3, or 4 minutes.
If the store opens at 8:00a.m. and random numbers are used to generate arrivals, what
time would the first customer arrive if the first random number were 02?
(a) 8:01
(b) 8:02
(c) 8:03
(d) 8:04
(e) none of the above
21. According to Table 15-3, the time between successive arrivals is 1, 2, 3, or 4 minutes.
The store opens at 8:00a.m. and random numbers are used to generate arrivals and
service times. The first random number to generate an arrival is 39, while the first
service time is generated by the random number 94. What time would the first
customer finish transacting business?
(a) 8:03
(b) 8:04
(c) 8:05
(d) 8:06
(e) none of the above
22. According to Table 15-3, the time between successive arrivals is 1, 2, 3, or 4 minutes.
The store opens at 8:00a.m. and random numbers are used to generate arrivals and
service times. The first 3 random numbers to generate arrivals are 09, 89, and 26.
What time does the third customer arrive?
(a) 8:07
(b) 8:08
(c) 8:09
(d) 8:10
(e) none of the above
23. According to Table 15-3, the time between successive arrivals is 1, 2, 3, or 4 minutes.
The store opens at 8:00a.m. and random numbers are used to generate arrivals and
service times. The first two random numbers for arrivals are 95 and 08. The first two
random numbers for service times are 92 and 18. At what time does the second
customer finish transacting business?
(a) 8:07
(b) 8:08
(c) 8:09
(d) 8:10
(e) none of the above
Table 15-4
Variable Value
Probability
Cumulative Probability
0
0.08
0.08
1
0.23
0.31
2
0.32
0.63
3
0.28
0.91
4
0.09
1.00
Number of Runs
200
Average Value
2.10
24. According to Table 15-4, which presents a summary of the Monte Carlo output from
a simulation of 200 runs, there are 5 possible values for the variable of concern. If
this variable represents the number of machine breakdowns during a day, what is the
probability that the number of breakdowns is 2 or fewer?
(a) 0.23
(b) 0.31
(c) 0.32
(d) 0.63
(e) none of the above
25. According to Table 15-4, which presents a summary of the Monte Carlo output from
a simulation of 200 runs, there are 5 possible values for the variable of concern. If
this variable represents the number of machine breakdowns during a day, what is the
probability that the number of breakdowns is more than 4?
(a) 0
(b) 0.08
(c) 0.09
(d) 1.00
(e) none of the above
26. According to Table 15-4, which presents a summary of the Monte Carlo output from
a simulation of 200 runs, there are 5 possible values for the variable of concern. If
this variable represents the number of machine breakdowns during a day, based on
this simulation run, what is the average number of breakdowns per day?
(a) 2.00
(b) 2.10
(c) 2.50
(d) 200
(e) none of the above
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