Table 1

Sample Size
n Mean Factor
A2 Upper Range
D4 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

1) Refer to Table 1. The Welldone Paint Company produces paint in gallon cans. They have found that in more than 10 samples of 9 cans each, the average gallon can contains 1.2 gallons of paint. The average range found over these samples is 0.17 gallons. What is the upper control limit for the sample averages in this process?
A) 1.100
B) 1.150
C) 1.268
D) 1.156
E) None of the above

2) Refer to Table 1. To guarantee that cans of pint are properly filled, some cans are sampled and the amounts measured. The overall average for the samples is 12 ounces. Each sample contains 7 cans. The average range is 0.5 ounces. The upper control chart limit for the sample averages would be
A) 12.1232.
B) 11.8768.
C) 13.2.
D) 12.308.
E) None of the above

3) Defects in computer hard-drives will usually render the entire computer worthless. For a particular model, the percent defective in the past has been 2%. If a sample size of 500 is taken, what would the 95.5% lower control chart limit be?
A) 0.00995
B) 0.00005
C) 0.01000
D) 0.09550
E) none of the above

4) A company has been receiving complaints about the attitude of some sales clerks. Over a 10-day period, the total number of complaints was 250. The company wishes to develop a control chart for the number of complaints. What would the upper control limit on the number of complaints per day be for a 3 sigma (99.5%) control chart?
A) 35
B) 40
C) 50
D) 200
E) None of the above

Table 2
Given the sample results (100 units in each sample):

Sample Number Number of Errors Fraction Defective
1 0 0.00
2 9 0.09
3 6 0.06
4 7 0.07
5 2 0.02
6 7 0.07
7 7 0.07
8 5 0.05
9 4 0.04
10 5 0.05

5) Refer to Table 2. Find the 99.5% lower limit of the appropriate p-chart.
A) 0.0076
B) 0.0964
C) 0.2014
D) 0.1397
E) None of the above

6) Markov analysis might be effectively used for
A) market share analysis.
B) university enrollment predictions.
C) machine breakdowns.
D) bad debt prediction.
E) All of the above

Table 3
The following data consists of a matrix of transition probabilities (P) of three competing companies, and the initial market share π(0). Assume that each state represents a company (Company 1, Company 2, Company 3, respectively) and the transition probabilities represent changes from one month to the next.

P = π(0) = (0.3, 0.6, 0.1)

7) Using the data in Table 3, and assuming that the transition probabilities do not change, in the long run what market share would Company 3 expect to reach? (Rounded to two decimal places.)
A) 0.30
B) 0.32
C) 0.39
D) 0.60
E) None of the above

8) The weather is becoming important to you since you would like to go on a picnic today. If it was sunny yesterday, there is a 75% chance it will be sunny today. If it was raining yesterday, there is a 40% chance it will be sunny today. If the probability that it was raining yesterday is 0.5, what is the probability that it will be sunny today?
A) 0.650
B) 0.390
C) 0.510
D) 0.490
E) None of the above

Table 4
A new young mother has opened a cloth diaper service. She is interested in simulating the number of diapers required for a one-year- old. She hopes to use this data to show the cost effectiveness of cloth diapers. The table below shows the number of diapers demanded daily and the probabilities associated with each level of demand.

Daily Demand Probability Interval of 
Random Numbers
5 0.30 01-30
6 0.50 31-80
7 0.05 81-85
8 0.15 86-00

9) According to Table 4, if the random number 83 were generated for a particular day, what would the simulated demand be for that day?
A) 5
B) 6
C) 7
D) 20
E) None of the above

10) According to Table 4, what is the cumulative probability that demand is less than or equal to 6?
A) 0.85
B) 0.95
C) 0.80
D) 0.15
E) None of the above

Table 5
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

11) According to Table 5, the number of arrivals in any 10-minute period is between 6 and 10, inclusive. Suppose the next three random numbers were 13, 75, and 41, 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

12) Which of the following is true about departures?
A) Random departures are independent of each other.
B) Random departures cannot be predicted exactly.
C) The Poisson distribution is often used to represent the departure pattern.
D) Service times often follow the negative exponential distribution.
E) The binomial distribution is often used to represent the departure pattern.

13) The customer who arrives at a bank initially joins a long line, but then, after a few momemnts leaves to return another time is
A) balking.
B) cropping.
C) reneging.
D) blithering.
E) None of the above

14) Which of the following is an assumption in common queuing mathematical models?
A) Arrivals come from a finite population.
B) Arrivals are negatively exponentially distributed.
C) Arrivals are free to balk or renege.
D) Service rates follow the Poisson distribution.
E) The average service rate is faster than the average arrival rate.

15) 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 7 per hour and the service rate is 2 every 10 minutes, what is the average number of customers in the system?
A) 0.50
B) 4.00
C) 2.25
D) 3.00
E) None of the above

16) 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 is the average number of customers waiting in line behind the person being served?
A) 0.50
B) 0.75
C) 2.25
D) 3.00
E) None of the above

17) Customers enter the waiting line at a cafeteria on a first-come, first-served basis. The arrival rate follows a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is four per minute and the average service rate of a single server is seven per minute, what is the average number of customers in the system?
A) 0.43
B) 1.67
C) 0.57
D) 1.33
E) None of the above

18) Which of the following distributions is most often used to estimate departure patterns?
A) negative exponential
B) normal
C) Poisson
D) Erlang
E) beta

19) 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

20) Slack time in a network is the
A) amount of time that an activity would take assuming very unfavorable conditions.
B) shortest amount of time that could be required to complete the activity.
C) amount of time that you would expect it would take to complete the activity.
D) difference between the expected completion time of the project using pessimistic times and the expected completion time of the project using optimistic times.
E) amount of time that an activity can be delayed without delaying the entire project.

21) Which of the following is not a concept associated with CPM?
A) normal time
B) probability
C) normal cost
D) crash cost
E) deterministic network

22) CPM
A) assumes we do not know ahead of time what activities must be completed.
B) assumes that activity time estimates follow the normal probability distribution.
C) is a deterministic network technique that allows for project crashing.
D) is a network technique that allows three time estimates for each activity in a project.
E) None of the above

23) The expected time in PERT is
A) a weighted average of the most optimistic time, most pessimistic time, and four times the most likely time.
B) the modal time of a beta distribution.
C) a simple average of the most optimistic, most likely, and most pessimistic times.
D) the square root of the sum of the variances of the activities on the critical path.
E) None of the above

24) Given an activity’s optimistic, most likely, and pessimistic time estimates of 3, 7, and 19 days respectively, compute the PERT expected activity time for this activity.
A) 6
B) 7
C) 9
D) 5
E) None of the above

25) Given an activity’s optimistic, most likely, and pessimistic time estimates of 6, 13, and 24 days respectively, compute the PERT variance for this activity.
A) 3
B) 6
C) 9
D) 18
E) None of the above

26) Given an activity’s optimistic, most likely, and pessimistic time estimates of 3, 5, and 15 days, respectively, compute the PERT standard deviation for this activity.
A) 2
B) 4
C) 5
D) 15
E) None of the above 

27) Given the following small project, the critical path is ________ days.

Activity Immediate
Predecessor Time
(days)
A – 8
B A 4
C – 10

A) 4
B) 10
C) 12
D) 22
E) None of the above

Table 6
The following represents a project with know 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

28) Using the data in Table 6, 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

29) Using the data in Table 12-1, compute the latest finish time for activity E.
A) 4
B) 10
C) 14
D) 25
E) None of the above

Table 7
The following represents a project with four activities. 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

30) According to the data in Table 7, what is the minimum expected completion time for the project?
A) 18
B) 19
C) 37
D) 11
E) None of the above

31) According to Table 7, 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. What is the probability that the project is finished in 16 weeks or fewer? (Round to two decimals.)
A) 0.07
B) 0.93
C) 0.43
D) 0.77
E) None of the above

Table 8

Activity Immediate
Predecessor Optimistic Most
Likely Pessimistic Standard
Deviation Variance
A — 4 5 6 0.333 0.111
B — 12 16 18 1.000 1.000
C A 2 8 14 2.000 4.000
D A 5 5 5 0.000 0.000
E B, C 6 7 8 0.333 0.111

32) According to Table 8, there are five activities in a PERT project. Which activities are on the critical path?
A) A-B-C-D-E
B) A-C-E
C) B-D
D) A-B-C-D
E) B-E

33) The critical path of a network is the
A) path with the least variance.
B) path with zero slack.
C) path with the most activities.
D) path with the largest variance.
E) None of the above

34) The work breakdown structure involves identifying the ________ for each activity.
A) time
B) cost
C) resource requirements
D) predecessors
E) All of the above

35) CPM stands for ________.
A) critical path management
B) critical project management
C) critical project method
D) critical path method
E) centralized project management

36) The two common techniques for drawing PERT networks are ________.
A) NOA and NRA
B) AON and AOA
C) GANTT and NOA
D) ONA and OAO
E) CAN and CAA

37) Given an activity’s optimistic, most likely, and pessimistic time estimates of 3, 7, and 11 days respectively, compute the expected time for this activity.
A) 5
B) 6
C) 7
D) 12
E) None of the above

38) Given an activity’s optimistic, most likely, and pessimistic time estimates of 3, 6, and 9 days respectively, compute the PERT variance for this activity.
A) 3
B) 1
C) 9
D) 6
E) None of the above

39) The project described by:

Activity Immediate 
Predecessor Time
(days)
A — 10
B A 4
C A 6
D B, C 7
E C 5

has a critical path of length of ________.
A) 21 days
B) 14 days
C) 23 days
D) 32 days
E) None of the above

40) 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.

41) Which of the following functions is nonlinear?
A) 4X + 2Y + 7Z
B) -4X + 2Y
C) 4X + (1/2)Y + 7Z
D) Z
E) 4X/Y + 7Z

42) A transportation problem is an example of
A) a pure-integer programming problem.
B) a mixed-integer programming problem.
C) a zero-one integer programming problem.
D) a goal programming problem.
E) a nonlinear programming problem.

Table 9

43) What is the total cost represented by the solution shown in Table 9?
A) 60
B) 2500
C) 2600
D) 500
E) None of the above

Table 10

44) In Table 10, cell A3 should be selected to be filled in the next solution. If this was selected as the cell to be filled, and the next solution was found using the appropriate stepping-stone path, how many units would be assigned to this cell?
A) 10
B) 15
C) 20
D) 30
E) None of the above

The following improvements are provided for Table 11:

Cell Improvement Index
A1 +2
A3 +6
B2 +1
B-Dummy +2
C1 +2
C2 +1

45) The cell improvement indices for Table 11 suggest that the optimal solution has been found. Based on this solution, how many units would actually be sent from source B?
A) 10
B) 170
C) 180
D) 250
E) None of the above

46) Transportation models can be used for which of the following decisions?
A) facility location
B) production mix
C) media selection
D) portfolio selection
E) employee shift scheduling

47) The only restriction we place on the initial solution of a transportation problem is that
A) we must have nonzero quantities in a majority of the boxes.
B) all constraints must be satisfied.
C) demand must be less than supply.
D) we must have a number (equal to the number of rows plus the number of columns minus one) of boxes that contain nonzero quantities.
E) None of the above

48) Which of the following statements concerning the transshipment problem are false?
A) The number of units shipped into a transshipment point should be equal to the number of units shipped out.
B) There can be constraints on the number of units shipped out of an origin point.
C) There can be constraints on the number of units shipped into a destination point.
D) The transshipment problem can be solved with linear programming.
E) Any units shipped from one origin point must all go to the same destination point.

49) What is the model called when total demand does not equal total supply in a transportation problem?
A) an unbalanced problem
B) an equilibrialized problem
C) a harmonized problem
D) a balanced problem
E) This situation can never occur.

50) Which of the following statements concerning transportation and assignment models is false?
A) The transportation, transshipment, and assignment problems can all be solved using linear programming.
B) A common objective is cost minimization.
C) Both transportation and assignment models involve the distribution of goods from sources to destinations.
D) The assignment problem can have a maximization objective.
E) The transshipment problem is a special class of transportation problems.