Operations Management Exam 3

1. 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.

The critical path is A-B-C, duration 15.

The critical path is A-C, duration 12.

The critical path is A-B-C, duration 13.5

The critical path cannot be determined without knowing PERT expected activity times.

The network has no critical path.

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.

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.

2. 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.

The critical path is D-E-F, duration 15.

The critical path is D-F, duration 12.

Slack at D is 3 units

Slack at E is 3 units

Both a and c are true

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.

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.

3. 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.

There are two paths in this network.

There are four paths in this network.

There are five paths in this network.

There are 25 paths through this network.

None of these statements is true.

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."

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."

4. A code of ethics especially for project managers

Has been established by the Project Management Institute

Has been formulated by the Federal government

Has been formulated by the World Trade Organization

Is inappropriate, since everyone should use the same guidance on ethical issues

Does not exist at this time

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.

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.

5. The region which satisfies all of the constraints in graphical linear programming is called the

Area of optimal solutions

Area of feasible solutions

Profit maximization space

Region of optimality

Region of non-negativity

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.

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.

6. Which of the following represents valid constraints in linear programming?

2X ≥ 7X*Y

2X * 7Y ≥ 500

2X + 7Y ≥ 100

2X2+ 7Y ≥ 50

All of the above are valid linear programming constraints.

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.

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.

7. Which of the following statements regarding Gantt charts is true?

Gantt charts give a timeline and precedence relationships for each activity of a project.

Gantt charts use the four standard spines of Methods, Materials, Manpower, and Machinery.

Gantt charts are visual devices that show the duration of activities in a project.

Gantt charts are expensive.

All of the above are true.

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.

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.

8. Which of the following statements regarding critical paths is true?

The shortest of all paths through the network is the critical path.

Some activities on the critical path may have slack.

Every network has exactly one critical path.

On a specific project, there can be multiple critical paths, all with exactly the same duration.

The duration of the critical path is the average duration of all paths in the project network.

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.

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.

9. 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

X = -1, y = 1

X = 0, y = 4

X = 2, y = 1

X = 5, y = 1

X = 2, y = 0

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.

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.

10. The corner point solution method requires

Finding the value of the objective function at the origin

Moving the iso-profit line to the highest level that still touch some part of the feasible region

Moving the iso-profit line to the lowest level that still touches some part of the feasible region

Finding the coordinates at each corner of the feasible solution space

None of the above

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.

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.

11. 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?

3X ≥ Y

X ≤ 3Y

X + Y ≥ 3

X – 3Y ≥ 0

3X ≤ Y

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.

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.

12. Which of the following statements regarding CPM networks is true?

There can be multiple critical paths on the same project, all with different durations.

The early finish of an activity is the latest early start of all preceding activities.

The late start of an activity is its late finish plus its duration.

If a specific project has multiple critical paths, all of them will have the same duration.

All of the above are true

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.

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.

13. 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

(0, 0), (50, 0), (0, 21), and (20, 15)

(0, 0), (70, 0), (25, 0), and (15, 20)

(20, 15)

(0, 0), (0, 100), and (210, 0)

None of the above

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.

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.

14. Which of the following is not a requirement of a linear programming problem?

An objective function, expressed in terms of linear equations

Constraint equations, expressed as linear equations

An objective function, to be maximized or minimized

Alternative courses of action

For each decision variable, there must be one constraint or resource limit

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.

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.

15. Which of the following statements about Bechtel is true?

Even though Bechtel is over 100 years old, the Kuwaiti oil fields was its first "project."

Bechtel is the world's premier manager of massive construction and engineering projects.

Bechtel's competitive advantage is supply chain management.

While its projects are worldwide, its network of suppliers is largely in the U.S.

All of the above are true

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.

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.

16. An iso-profit line

Can be used to help solve a profit maximizing linear programming problem

Is parallel to all other iso-profit lines in the same problem

Is a line with the same profit at all points

None of the above

All of the above

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.

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.

17. Which of the following combinations of constraints has no feasible region?

X + Y > 15 and X – Y < 10

X + Y > 5 and X > 10

X > 10 and Y > 20

X + Y > 100 and X + Y < 50

All of the above have a feasible region.

not-available-via-ai

Explanation

not-available-via-ai

18. In linear programming, a statement such as "maximize contribution" becomes a(n)

Constraint

Slack variable

Objective function

Violation of linearity

Decision variable

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.

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.

19. 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?

The shadow price of the added resource will rise.

The solution stays the same; the extra resource can't be used without more of the other scarce resource.

The extra resource will cause the value of the objective to fall.

The optimal mix will be rearranged to use the added resource, and the value of the objective function will rise.

None of the above

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.

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.

20. 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

X = 2, y = 1

X = 1, y = 5

X = -1, y = 1

X = 4, y = 4

X = 2, y = 8

?

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

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

21. 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.

X = 2, y = 0

X = 0, y = 3

X = 0, y = 0

X = 1, y = 5

None of the above

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.

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.

22. Which of the following sets of constraints results in an unbounded maximizing problem?

X + Y > 100 and X + Y < 50

X + Y > 15 and X – Y < 10

X + Y < 10 and X > 5

X < 10 and Y < 20

All of the above have a bounded maximum.

The set of constraints X + Y > 15 and X – Y

Explanation

The set of constraints X + Y > 15 and X – Y

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

Maximize $40Y = $25Z

Maximize $40Y + $25Z

Maximize $30Y + $20Z

Maximize 0.25Y + 0.20Z

None of the above

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.

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.

24. 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?

There are four corner points including (50, 0) and (0, 12.5).

The two corner points are (0, 0) and (50, 12.5).

The graphical origin (0, 0) is not in the feasible region.

The feasible region includes all points that satisfy one constraint, the other, or both.

The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.

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.

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.