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Quant. Analysis
• From Mathematics, Differential Analysis
• Due on 04 May, 2016 02:04:00
• Asked On 24 Apr, 2016 06:06:31
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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

(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

(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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