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Question

The first step in planning and scheduling a project is to develop the __________.

Student Answer:

employee scheduling plan

PERT/CPM network diagram

critical path

work breakdown structure

variance calculations for each activity

Question 2. The critical path of a network is the:

Student Answer:

shortest time path through the network.

path with the fewest activities.

path with the most activities.

longest time path through the network.

none of the above.

Question 3. PERT:

Student Answer:

assumes that we do not know ahead of time what activities must be completed.

assumes that activity time estimates follow the normal probability distribution.

is a network technique that uses three time estimates for each activity in a project.

is a deterministic network technique that allows for project crashing.

None of the above is correct.

Question 4. The following table represents a project with four activities. All times are in weeks.

The following represents a project with four a activities. All times are in weeks

Activity

Immediate Predecessor

Optimistic time

Most likely time

Pessimistic time

A

–

2

8

17

B

–

8

8

8

C

A

6

9

18

D

B

5

11

17

Using the data in the table, what is the minimal expected completion tiime (in weeks) for the project?

Student Answer:

18

19

37

11

None of the above

Question 5. A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. What is the average length of the line?

Student Answer:

3.429

1.929

1.143

0.643

None of the above

Question 6. Two characteristics of arrivals are the line length and queue discipline.

Student Answer:

True

False

Question 7. Which of the following questions can be answered by PERT?

Student Answer:

When will the entire project be completed?

What is the probability that the project will be completed by a specific date?

What are the critical activities?

What are the noncritical activities?

All of the above

Question 8. One difficulty in waiting line analysis is that it is sometimes difficult to place a value on customer waiting time.

Student Answer:

True

False

Question 9. If the total supply from the sources does not equal the total demand from the destinations in the transportation problem:

Student Answer:

and if supply is greater than demand, add a dummy source or factory.

the amount put in a dummy source or destination should make supply and demand equal.

and if demand is greater than supply, add a dummy destination or warehouse.

all of the above.

none of the above.

Question 10. Consider the following linear programming model:

Maximize X12 + X2 + 3X3

Subject to:

X1 + X2 ≤ 3

X1 + X2 ≤ 1

X1, X2 ≥ 0

This problem violates which of the following assumptions?

Student Answer: Certainty

Proportionality

Divisibility

Linearity

Integrality

Question 11. A company must assign mechanics to each of four jobs.

Click here to view an Excel version of the table.

The time involved varies according to individual abilities.The table shows how many minutes it takes each mechanic to perform each job. If the optimal assignments are made, how many total minutes would be required for completing the jobs?

Student Answer:

0

4

17

16

None of the above

Question 12. Transportation models can be used for which of the following decisions?

Student Answer:

Facility location

Production mix

Media selection

Portfolio selection

Employee shift scheduling

Question 13. Consider the following linear programming problem:

Maximize 4X + 10Y

Subject to:

3X + 4Y ≤ 480

4X + 2Y ≤ 360

all variables ≥ 0

The feasible corner points are (48,84), (0,120), (0,0), (90,0). What is the maximum possible value for the objective function?

Student Answer:

1,032

1,200

360

1,600

None of the above

Question 14. Variations that need not occur in production processes are referred to as _______.

Student Answer:

assignable variations

control variations

natural variations

process variations

none of the above

Question 15. The following table represents a project with known activity times. All times are in weeks.

**Use table below to answer question**

**The following represents a project with known activity times. All times are in weeks.**

**Activity**

**Immediate**

**Predecessor**

**Time**

A

–

4

B

–

3

C

2

D

A

7

E

B

4

F

C, D

5

G

B

4

Using the data in the table, what is the latest possible time (in weeks) that C may be started without delaying completion of the project?

Student Answer:

0

4

8

10

None of the above

Question 16. The p-chart is useful when we:

Student Answer:

take a number of measurements and compute the average.

take a number of measurements and compute the ranges.

find the fraction of the production lot defective.

find the number of defective items in a production lot.

None of the above is correct.

Question 17. Which of the following is not an assumption of LP?

Student Answer:

Simultaneity

Certainty

Proportionality

Divisibility

Additivity

Question 18. Bank Boston has a branch at Bryant College. The branch is busiest at the beginning of the college year when freshmen and transfer students open accounts. This year, freshmen arrived at the office at a rate of 40 per day (assume 8-hour days). On average, it takes the Bank Boston staff person about ten minutes to process each account application. The bank is considering having one or two tellers. Each teller is paid $12 per hour and the cost of waiting in line is assumed to be $8 per hour.

Which model is preferred?

Student Answer:

One-channel

Two-channel

Both are the same

Question 19. A certain firm has four different operations that must be assigned to four locations. The profit (in thousands of dollars) associated with each operation at each location is presented below. The firm’s vice president would like to assign the various operations so that the total profit is maximized. Find the appropriate assignments.

Operation

Location

1

2

3

4

W

9

11

7

10

X

10

12

6

12

Y

8

10

13

9

Z

12

8

11

10

Using the data in the table, what is the optimal location for Operation Z?

Student Answer:

1

2

3

4

Question 20. A feasible solution to a linear programming problem:

Student Answer: must be a corner point of the feasible region.

must satisfy all of the problem’s constraints simultaneously.

need not satisfy all of the constraints, only the non-negativity constraints.

must give the maximum possible profit.

must give the minimum possible cost.

Question 21. Management resources that need control include machinery usage, labor volume, money spent, time used, warehouse space used, and material usage.

Student Answer:

True

False

Question 22. The following table represents a project with four activities. All times are in weeks.

The following represents a project with known activity times. All times are in weeks.

Activity

Immediate

Predecessor

Optimistic Time

Most Likely Time

Pessimistic Time

A

–

2

8

14

B

–

8

8

8

C

A

6

9

18

D

B

5

11

17

According to the data in the table, there are four activities in the project. Assume the normal distribution is appropriate to use to determine the probability of finishing by a particular time. If you wished to find the probability of finishing the project in 20 weeks or fewer, it would be necessary to find the variance and then the standard deviation to be used with the normal distribution. What variance would be used?

Student Answer:

2

4

8

12

None of the above

Question 23. Which tableau is the solution to the following transportation table?

Click here to view a Word version of the table.

Student Answer:

Choice A

Choice B

Choice C

Choice D

None of the above

Question 24. The maximal-flow model assumes that there is a net flow from “source” to “sink.”

Student Answer:

True

False

Question 25. An automatic car wash is an example of a constant service time model.

Student Answer:

True

False

Question 26. The points on the network are referred to as nodes.

Student Answer:

True

False

Question 27. Click here to view a Word version of the table.

Bags of chocolate candy are sampled to ensure proper weight. The overall average for the samples is 36 ounces. Each sample contains twelve bags. The average range is 1.3 ounces.

Sample Size n

Mean Factor A2

Upper Range D2

Lower Range D3

2

1.880

3.628

0

3

1.023

2.574

0

4

0.729

2.282

0

5

0.577

2.114

0

6

0.483

2.004

0

7

0.419

1.924

0.076

8

0.373

1.864

0.136

9

0.337

1.816

0.184

10

0.308

1.777

0.223

12

0.266

1.716

0.284

Using the data in the table above, what is the upper control chart limit for the sample averages?

Student Answer:

36.3458

35.6542

38.3101

36.6279

37.1258

Question 28. A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution while service times follow an exponential distribution. If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, how much time will elapse (in hours) from the time a customer enters the line until he/she leaves the restaurant?

Student Answer:

0.50

0.25

0.75

2.25

3.00

Question 29. Frequently in queuing problems, the number of arrivals per unit of time can be estimated by a probability distribution known as the Poisson distribution.

Student Answer:

True

False

Question 30. When using a general LP model for transportation problems, if there are 4 sources and 3 destinations, which of the following statements is true?

Student Answer:

There are typically 4 decision variables and 3 constraints.

There are typically 12 decision variables and 7 constraints.

There are typically 7 decision variables and 7 constraints.

There are typically 12 decision variables and 12 constraints.

There are typically 12 decision variables and 3 constraints.

Question 31. The c-chart is useful when we:

Student Answer:

take a number of measurements and compute the average.

take a number of measurements and compute the ranges.

find the fraction of the production lot defective.

find the number of defective items in a production lot.

None of the above is correct.

Question 32. PERT stands for __________.

Student Answer:

probabilistic evaluation and review technique

program evaluation and review technique

probability of expected run times

program of expected run times

project evaluation and review technique

Question 33. A company can decide how many additional labor hours to acquire for a given week. Subcontractor workers will only work a maximum of 20 hours a week. The company must produce at least 200 units of product A, 300 units of product B, and 400 units of product C. In 1 hour of work, worker 1 can produce 15 units of product A, 10 units of product B, and 30 units of product C. Worker 2 can produce 5 units of product A, 20 units of product B, and 35 units of product C. Worker 3 can produce 20 units of product A, 15 units of product B, and 25 units of product C. Worker 1 demands a salary of $50/hr, worker 2 demands a salary of $40/hr, and worker 3 demands a salary of $45/hr. The company must choose how many hours they should contract with each worker to meet their production requirements and minimize labor cost.

Assuming this is a linear programming problem, which of the following is the optimal solution?

Student Answer:

X1 = 7.69; X2 = 0; X3 = 9.23

X1 = 0; X2 = 7.69; X3 = 9.23

X1 = 0; X2 = 9.23; X3 = 7.69

X1 = 9.23; X2 = 7.69; X3 = 0

Question 34. According to the table below, there are five activities in a PERT project.

Click here to view a Word version of the table.

Using the data in the table, what is the variance of the critical path?

Student Answer:

a. 5.222

b. 1.111

c. 1.222

d. 0

e. 4.222

Question 35. Infeasibility in a linear programming problem occurs when:

Student Answer: there is an infinite solution.

a constraint is redundant.

more than one solution is optimal.

the feasible region is unbounded.

there is no solution that satisfies all the constraints given.

Question 36. In PERT, we assume that:

Student Answer:

the times to complete individual activities are known with certainty.

all activities are carried out by staff from our own organization.

the total cost of a project is independent of the time to complete the project.

the total time to complete all activities on the critical path is described by a normal distribution.

none of the above.

Question 37. Bank Boston has a branch at Bryant College. The branch is busiest at the beginning of the college year when freshmen and transfer students open accounts. This year, freshmen arrived at the office at a rate of 40 per day (assume 8-hour days). On average, it takes the Bank Boston staff person about ten minutes to process each account application. The bank is considering having one or two tellers. Each teller is paid $12 per hour and the cost of waiting in line is assumed to be $8 per hour.

What is the total daily waiting cost for the two-teller model?

Student Answer:

$4.17

$11.20

$133.32

$266.56

Total waiting cost = [(5 x 0.35 hours) (8)] x 8 hours/day = $11.20

Question 38. The maximal-flow technique finds the maximum flow of any quantity or substance through a network.

Student Answer:

True

False

Question 39. If items being transported must go through an intermediate point before reaching a final destination, then this situation is known as a(n) __________.

Student Answer:

transshipment problem

assignment problem

transportation problem

intermediate point problem

None of the above

Question 40. Which of the following is not true about arrivals?

Student Answer:

Random arrivals are independent of each other.

Random arrivals cannot be predicted exactly.

The Poisson distribution is often used to represent the arrival pattern.

Service times often follow the negative exponential distribution.

The exponential distribution is often used to represent the arrival pattern.

Question 41. Consider the following linear programming problem:

Minimize 20X + 30Y

Subject to:

2X + 4Y < 800

6X + 3Y > 120

X, Y > 0

What is the optimum solution to this problem (X,Y)?

Student Answer:

(0,0)

(50,0)

(0,100)

(400,0)

None of the above

Question 42. A goal of many waiting line problems is to help a firm find the ideal level of services that minimize the cost of waiting and the cost of providing the service.

Student Answer:

True

False

Question 43. An arrival in a queue that reneges is one who:

Student Answer:

after joining the queue, becomes impatient and leaves.

refuses to join the queue because it is too long.

goes through the queue, but never returns.

jumps from one queue to another, trying to get through as quickly as possible.

None of the above is correct.

Question 44. A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution while service times follow an exponential distribution. If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, what proportion of the time is the server busy?

Student Answer:

0.25

0.50

0.75

2.25

3.00

Question 45. In a single-channel, single-phase system, reducing the service time only reduces the total amount of time spent in the system, not the time spent in the queue.

Student Answer:

True

False

Question 46. Which of the following is a basic assumption of linear programming?

Student Answer: The condition of uncertainty exists.

Independence exists for the activities.

Proportionality exists in the objective function and constraints.

Divisibility does not exist, allowing only integer solutions.

Solutions or variables may take values from -? to +?.

Question 47. A widely used mathematical programming technique designed to help managers and decision making relative to resource allocation is called __________.

Student Answer:

linear programming

computer programming

constraint programming

goal programming

None of the above

Question 48. When receiving a shipment from a supplier, inspection must be done to check the fraction of defective products. This is best monitored by which of the following control charts?

Student Answer:

x-bar chart

R-chart

p-chart

c-chart

None of the above

Question 49. The work breakdown structure involves identifying the __________ for each activity.

Student Answer:

time

cost

resource requirements

predecessors

all of the above

Question 50. Technically, to achieve Six Sigma quality, there would have to be fewer than __________ defects per million opportunities.

Student Answer:

6

166,667

667

67

3.4

3

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