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Which of the following statements about Bechtel is true?
A.
Even though Bechtel is over 100 years old, the Kuwaiti oil fields was its first "project."
B.
Bechtel is the world's premier manager of massive construction and engineering projects.
C.
Bechtel's competitive advantage is supply chain management.
D.
While its projects are worldwide, its network of suppliers is largely in the U.S.
E.
All of the above are true
Correct Answer B. Bechtel is the world's premier manager of massive construction and engineering projects.
Explanation Bechtel is known for being the world's premier manager of massive construction and engineering projects. This means that they are highly respected and recognized for their expertise in overseeing and successfully completing large-scale projects in the construction and engineering industry.
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2.
A code of ethics especially for project managers
A.
Has been established by the Project Management Institute
B.
Has been formulated by the Federal government
C.
Has been formulated by the World Trade Organization
D.
Is inappropriate, since everyone should use the same guidance on ethical issues
E.
Does not exist at this time
Correct Answer A. Has been established by the Project Management Institute
Explanation The correct answer is "has been established by the Project Management Institute." This means that the Project Management Institute has created a specific code of ethics for project managers. This implies that project managers should adhere to this code of ethics in their professional practice.
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3.
Which of the following statements regarding Gantt
charts is true?
A.
Gantt charts give a timeline and precedence relationships for each activity of a project.
B.
Gantt charts use the four standard spines of Methods, Materials, Manpower, and Machinery.
C.
Gantt charts are visual devices that show the duration of activities in a project.
D.
Gantt charts are expensive.
E.
All of the above are true.
Correct Answer C. Gantt charts are visual devices that show the duration of activities in a project.
Explanation Gantt charts are visual devices that show the duration of activities in a project. They provide a graphical representation of the project schedule, displaying the start and end dates of each activity. Gantt charts are helpful in visualizing the timeline and identifying any overlapping or conflicting activities. They do not use the four standard spines mentioned in the second option, nor are they necessarily expensive. Therefore, the correct answer is that Gantt charts are visual devices that show the duration of activities in a project.
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4.
Which of the following statements regarding critical
paths is true?
A.
The shortest of all paths through the network is the critical path.
B.
Some activities on the critical path may have slack.
C.
Every network has exactly one critical path.
D.
On a specific project, there can be multiple critical paths, all with exactly the same duration.
E.
The duration of the critical path is the average duration of all paths in the project network.
Correct Answer D. On a specific project, there can be multiple critical paths, all with exactly the same duration.
Explanation The statement that is true regarding critical paths is that on a specific project, there can be multiple critical paths, all with exactly the same duration. This means that there can be more than one sequence of activities that are critical and have the same total duration, meaning that any delay in these activities will result in a delay in the overall project. This is important to consider when planning and managing a project, as it highlights the need to focus on all critical paths to ensure timely completion.
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5.
A simple CPM network has three activities, A, B,
and C. A is an immediate predecessor of B and of
C. B is an immediate predecessor of C. The activity
durations are A=4, B=3, C=8.
A.
The critical path is A-B-C, duration 15.
B.
The critical path is A-C, duration 12.
C.
The critical path is A-B-C, duration 13.5
D.
The critical path cannot be determined without knowing PERT expected activity times.
E.
The network has no critical path.
Correct Answer A. The critical path is A-B-C, duration 15.
Explanation The critical path is determined by identifying the longest path in the network, which represents the total duration of the project. In this case, the critical path is A-B-C, with durations of 4+3+8=15. This means that any delay in any of these activities will directly impact the overall project duration.
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6.
A simple CPM network has three activities, D, E,
and F. D is an immediate predecessor of E and of F.
E is an immediate predecessor of F. The activity
durations are D=4, E=3, F=8.
A.
The critical path is D-E-F, duration 15.
B.
The critical path is D-F, duration 12.
C.
Slack at D is 3 units
D.
Slack at E is 3 units
E.
Both a and c are true
Correct Answer A. The critical path is D-E-F, duration 15.
Explanation The critical path is the longest path in a project network that determines the total duration of the project. In this case, the critical path is D-E-F, with durations of 4, 3, and 8 units respectively, totaling 15 units. This means that any delay in any of these activities will directly impact the total duration of the project. Therefore, the given answer is correct.
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7.
A simple CPM network has five activities, A, B, C,
D, and E. A is an immediate predecessor of C and
of D. B is also an immediate predecessor of C and
of D. C and D are both immediate predecessors of
E.
A.
There are two paths in this network.
B.
There are four paths in this network.
C.
There are five paths in this network.
D.
There are 25 paths through this network.
E.
None of these statements is true.
Correct Answer B. There are four paths in this network.
Explanation The given network has five activities: A, B, C, D, and E. A and B are both immediate predecessors of C and D. C and D are both immediate predecessors of E. Since there are two options for the immediate predecessors of C (A and B) and two options for the immediate predecessors of D (A and B), there are four possible paths in this network: A-C-E, A-D-E, B-C-E, and B-D-E. Therefore, the correct answer is "There are four paths in this network."
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8.
Which of the following statements regarding CPM
networks is true?
A.
There can be multiple critical paths on the same project, all with different durations.
B.
The early finish of an activity is the latest early start of all preceding activities.
C.
The late start of an activity is its late finish plus its duration.
D.
If a specific project has multiple critical paths, all of them will have the same duration.
E.
All of the above are true
Correct Answer D. If a specific project has multiple critical paths, all of them will have the same duration.
Explanation In a CPM (Critical Path Method) network, the critical path is the longest path through the project network and determines the project duration. It consists of activities that have zero slack or float, meaning any delay in these activities will directly impact the project duration. If a specific project has multiple critical paths, it means there are multiple paths with zero slack. Since these paths have zero slack, any delay in any of the activities on these paths will result in a delay in the project duration. Therefore, all of the critical paths in a specific project will have the same duration.
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9.
Which of the following represents valid constraints in linear programming?
A.
2X ≥ 7X*Y
B.
2X * 7Y ≥ 500
C.
2X + 7Y ≥ 100
D.
2X2+ 7Y ≥ 50
E.
All of the above are valid linear programming constraints.
Correct Answer C. 2X + 7Y ≥ 100
Explanation The given inequality 2X + 7Y ≥ 100 represents a valid constraint in linear programming. In linear programming, constraints are inequalities that restrict the feasible region of the problem. This constraint states that the sum of 2 times X and 7 times Y must be greater than or equal to 100. It sets a lower bound on the possible values of X and Y in order to satisfy the constraint.
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10.
Which of the following is not a requirement of a linear programming problem?
A.
An objective function, expressed in terms of linear equations
B.
Constraint equations, expressed as linear equations
C.
An objective function, to be maximized or minimized
D.
Alternative courses of action
E.
For each decision variable, there must be one constraint or resource limit
Correct Answer E. For each decision variable, there must be one constraint or resource limit
Explanation A requirement of a linear programming problem is that for each decision variable, there must be one constraint or resource limit. This means that each decision variable must have a corresponding constraint that limits its value. The other options mentioned in the question are all requirements of a linear programming problem. The objective function must be expressed in terms of linear equations, the constraint equations must also be expressed as linear equations, and there must be alternative courses of action to choose from.
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11.
In linear programming, a statement such as "maximize contribution" becomes a(n)
A.
Constraint
B.
Slack variable
C.
Objective function
D.
Violation of linearity
E.
Decision variable
Correct Answer C. Objective function
Explanation In linear programming, an objective function is used to maximize or minimize a certain quantity, such as profit or cost. It represents the goal or objective of the problem and is typically stated as "maximize" or "minimize" followed by a specific quantity. Therefore, the statement "maximize contribution" would be transformed into an objective function in linear programming.
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12.
An iso-profit line
A.
Can be used to help solve a profit maximizing linear programming problem
B.
Is parallel to all other iso-profit lines in the same problem
C.
Is a line with the same profit at all points
D.
None of the above
E.
All of the above
Correct Answer E. All of the above
Explanation An iso-profit line can be used to help solve a profit maximizing linear programming problem because it represents all the combinations of inputs that yield the same profit. It is parallel to all other iso-profit lines in the same problem because they all represent the same profit level. Additionally, an iso-profit line is a line with the same profit at all points, as it represents the combinations of inputs that result in the same profit. Therefore, all of the given statements are correct.
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13.
Which of the following combinations of constraints has no feasible region?
A.
X + Y > 15 and X – Y < 10
B.
X + Y > 5 and X > 10
C.
X > 10 and Y > 20
D.
X + Y > 100 and X + Y < 50
E.
All of the above have a feasible region.
Correct Answer D. X + Y > 100 and X + Y < 50
14.
The corner point solution method requires
A.
Finding the value of the objective function at the origin
B.
Moving the iso-profit line to the highest level that still touch some part of the feasible region
C.
Moving the iso-profit line to the lowest level that still touches some part of the feasible region
D.
Finding the coordinates at each corner of the feasible solution space
E.
None of the above
Correct Answer D. Finding the coordinates at each corner of the feasible solution space
Explanation The corner point solution method involves finding the coordinates at each corner of the feasible solution space. By determining the values at these corners, the method allows for the identification of the optimal solution that maximizes or minimizes the objective function. This approach is based on the assumption that the optimal solution lies at one of the corner points of the feasible region. By evaluating the objective function at each corner point, the best solution can be determined.
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15.
Which of the following sets of constraints results in an unbounded maximizing problem?
A.
X + Y > 100 and X + Y < 50
B.
X + Y > 15 and X – Y < 10
C.
X + Y < 10 and X > 5
D.
X < 10 and Y < 20
E.
All of the above have a bounded maximum.
Correct Answer B. X + Y > 15 and X – Y < 10
Explanation The set of constraints X + Y > 15 and X – Y < 10 results in an unbounded maximizing problem because there are no upper or lower limits on the values of X and Y. The constraints allow for infinite combinations of X and Y that satisfy the inequalities, meaning there is no maximum value that can be reached. Therefore, the problem does not have a bounded maximum.
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16.
The region which satisfies all of the constraints in graphical linear programming is called the
A.
Area of optimal solutions
B.
Area of feasible solutions
C.
Profit maximization space
D.
Region of optimality
E.
Region of non-negativity
Correct Answer B. Area of feasible solutions
Explanation The region which satisfies all of the constraints in graphical linear programming is called the "area of feasible solutions". This refers to the set of all possible solutions that meet the given constraints. It represents the range of values that the decision variables can take while still satisfying all the constraints. The area of feasible solutions is the region in which the objective function can be optimized while adhering to the constraints.
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17.
For the two constraints given below, which point is in the feasible region of this maximization problem? (1) 14x + 6y <= 42
(2) x - y <=3
A.
X = 2, y = 1
B.
X = 1, y = 5
C.
X = -1, y = 1
D.
X = 4, y = 4
E.
X = 2, y = 8
F.
?
Correct Answer F. ?
Explanation The point x = 2, y = 1 is in the feasible region of this maximization problem because it satisfies both constraints. The first constraint, 14x + 6y
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18.
For the two constraints given below, which point is in the feasible region of this minimization problem? (1) 14x + 6y >= 42 (2) x - y >= 3
A.
X = -1, y = 1
B.
X = 0, y = 4
C.
X = 2, y = 1
D.
X = 5, y = 1
E.
X = 2, y = 0
Correct Answer D. X = 5, y = 1
Explanation The point (x = 5, y = 1) is in the feasible region because it satisfies both constraints. For the first constraint, when we substitute x = 5 and y = 1 into the equation 14x + 6y >= 42, we get 14(5) + 6(1) = 70, which is greater than or equal to 42. For the second constraint, when we substitute x = 5 and y = 1 into the equation x - y >= 3, we get 5 - 1 = 4, which is also greater than or equal to 3. Therefore, the point (x = 5, y = 1) satisfies both constraints and is in the feasible region.
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19.
What combination of x and y will yield the optimum for this problem?
Maximize $3x + $15y, subject to (1) 2x + 4y <= 12 and (2) 5x + 2y <= 10.
A.
X = 2, y = 0
B.
X = 0, y = 3
C.
X = 0, y = 0
D.
X = 1, y = 5
E.
None of the above
Correct Answer C. X = 0, y = 0
Explanation The given problem requires maximizing the objective function $3x + 15y$ while satisfying the given constraints. The constraints are represented by the inequalities $2x + 4y \leq 12$ and $5x + 2y \leq 10$. By substituting the values of x and y from the answer options, it can be observed that none of the options satisfy both constraints simultaneously. Therefore, none of the given combinations of x and y will yield the optimum for this problem.
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20.
A maximizing linear programming problem has two constraints: 2X + 4Y <= 100 and 3X + 10Y <= 210, in addition to constraints stating that both X and Y must be nonnegative. The corner points of the feasible region of this problem are
A.
(0, 0), (50, 0), (0, 21), and (20, 15)
B.
(0, 0), (70, 0), (25, 0), and (15, 20)
C.
(20, 15)
D.
(0, 0), (0, 100), and (210, 0)
E.
None of the above
Correct Answer A. (0, 0), (50, 0), (0, 21), and (20, 15)
Explanation The corner points of the feasible region are the points where the constraints intersect. By graphing the constraints, it can be observed that the points (0, 0), (50, 0), (0, 21), and (20, 15) are the only points that satisfy all the constraints. Therefore, these are the corner points of the feasible region.
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21.
A linear programming problem has two constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100. Which of the following statements about its feasible region is true?
A.
There are four corner points including (50, 0) and (0, 12.5).
B.
The two corner points are (0, 0) and (50, 12.5).
C.
The graphical origin (0, 0) is not in the feasible region.
D.
The feasible region includes all points that satisfy one constraint, the other, or both.
E.
The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.
Correct Answer A. There are four corner points including (50, 0) and (0, 12.5).
Explanation The feasible region in a linear programming problem is the set of all points that satisfy all the constraints. In this case, the two constraints are 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100. To find the corner points of the feasible region, we need to find the intersection points of the lines formed by each constraint. By solving the system of equations, we can determine that the corner points are (50, 0), (0, 12.5), (0, 0), and another point that is not mentioned in the question. Therefore, the statement that there are four corner points including (50, 0) and (0, 12.5) is true.
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22.
A linear programming problem contains a restriction that reads "the quantity of X must be at least three times as large as the quantity of Y." Which of the following inequalities is the proper formulation of this constraint?
A.
3X ≥ Y
B.
X ≤ 3Y
C.
X + Y ≥ 3
D.
X – 3Y ≥ 0
E.
3X ≤ Y
Correct Answer D. X – 3Y ≥ 0
Explanation The correct answer is X - 3Y ≥ 0. This inequality represents the restriction that the quantity of X must be at least three times as large as the quantity of Y. By subtracting 3Y from X and setting it greater than or equal to 0, we ensure that X is at least three times as large as Y.
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23.
A firm makes two products, Y and Z. Each unit of Y costs $10 and sells for $40. Each unit of Z costs $5 and sells for $25. If the firm's goal were to maximize sales revenue, the appropriate objective function would be
A.
Maximize $40Y = $25Z
B.
Maximize $40Y + $25Z
C.
Maximize $30Y + $20Z
D.
Maximize 0.25Y + 0.20Z
E.
None of the above
Correct Answer C. Maximize $30Y + $20Z
Explanation The appropriate objective function to maximize sales revenue can be determined by considering the cost and selling price of each product. Since each unit of Y costs $10 and sells for $40, the profit per unit of Y is $30 ($40 - $10). Similarly, each unit of Z costs $5 and sells for $25, resulting in a profit per unit of Z of $20 ($25 - $5). To maximize sales revenue, we need to maximize the total profit, which is given by $30Y + $20Z. Therefore, the correct answer is to maximize $30Y + $20Z.
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24.
A linear programming maximization problem has been solved. In the optimal solution, two resources are scarce. If an added amount could be found for only one of these resources, how would the optimal solution be changed?
A.
The shadow price of the added resource will rise.
B.
The solution stays the same; the extra resource can't be used without more of the other scarce resource.
C.
The extra resource will cause the value of the objective to fall.
D.
The optimal mix will be rearranged to use the added resource, and the value of the objective function will rise.
E.
None of the above
Correct Answer D. The optimal mix will be rearranged to use the added resource, and the value of the objective function will rise.
Explanation If an added amount could be found for only one of the scarce resources, the optimal solution would be changed by rearranging the mix to use the added resource. This means that the added resource would be utilized in the optimal solution, leading to an increase in the value of the objective function.