Ch14 Test Bank Docx Tools Linear Programming

CHAPTER 14 SUPPLEMENT

OPERATIONAL DECISION-MAKING TOOLS: LINEAR PROGRAMMING

CHAPTER LEARNING OBJECTIVES

Linear programming is one of several related quantitative techniques that are generally classified as mathematical programming models. Other quantitative techniques that fall into this general category include integer programming, nonlinear programming, and goal or multiobjective programming. These modeling techniques are capable of addressing a large variety of complex operational decision-making problems, and they are used extensively to do so by businesses and companies around the world. Computer software packages are available to solve most of these types of models, which greatly promotes their use.

TRUE-FALSE STATEMENTS

1. Operations managers find very few types of linear program models applicable today because finding an optimal solution is no longer a concern.

Answer: False

Difficulty: Easy

Learning Objective: Formulate a basic linear programming model including the definition of decision variables, objective function, and constraints.

Section Reference: S14.1 Model Formulation

2. In general, the objective function for linear programming problems in operations is one of minimizing costs.

Answer: True

Difficulty: Medium

Learning Objective: Formulate a basic linear programming model including the definition of decision variables, objective function, and constraints.

Section Reference: S14.1 Model Formulation

3. A formulation for a linear programming model consists of a decision variable, a constraint, and several objective functions.

Answer: False

Difficulty: Easy

Learning Objective: Formulate a basic linear programming model including the definition of decision variables, objective function, and constraints.

Section Reference: S14.1 Model Formulation

4. The objective function is a linear relationship that either minimizes or maximizes some value.

Answer: True

Difficulty: Easy

Learning Objective: Formulate a basic linear programming model including the definition of decision variables, objective function, and constraints.

Section Reference: S14.1 Model Formulation

5. The formulation for a linear programming problem cannot include more than one decision variable.

Answer: False

Difficulty: Easy

Learning Objective: Formulate a basic linear programming model including the definition of decision variables, objective function, and constraints.

Section Reference: S14.1 Model Formulation

6. The constraints in a linear programming formulation define the feasible solution space.

Answer: True

Difficulty: Easy

Learning Objective: Formulate a basic linear programming model including the definition of decision variables, objective function, and constraints.

Section Reference: S14.1 Model Formulation

7. Linear programming is a mathematical modelling technique based on linear relationships.

Answer: True

Difficulty: Easy

Learning Objective: Formulate a basic linear programming model including the definition of decision variables, objective function, and constraints.

Section Reference: S14.1 Model Formulation

8. While all linear programming problems have a single objective function, very few, if any, have constraints.

Answer: False

Difficulty: Easy

Learning Objective: Formulate a basic linear programming model including the definition of decision variables, objective function, and constraints.

Section Reference: S14.1 Model Formulation

9. A linear programming model’s constraints are nonlinear relationships that describe the restrictions placed on the decision variables.

Answer: False

Difficulty: Medium

Learning Objective: Formulate a basic linear programming model including the definition of decision variables, objective function, and constraints.

Section Reference: S14.1 Model Formulation

10. Linear programming problems with two decision variables can be solved graphically.

Answer: True

Difficulty: Medium

Learning Objective: Determine the optimal solution for a linear programming model with two decision variables using the graphical solution method.

Section Reference: S14.2 Graphical Solution Method

11. Most real-world linear programming problems are solved graphically.

Answer: False

Difficulty: Easy

Learning Objective: Determine the optimal solution for a linear programming model with two decision variables using the graphical solution method.

Section Reference: S14.2 Graphical Solution Method

12. The feasible solution space contains the values for the decision variables that satisfy the majority of the linear programming model’s constraints.

Answer: False

Difficulty: Medium

Learning Objective: Calculate unused or surplus resources given a model solution and provide an overview of the simplex method.

Section Reference: S14.3 Linear Programming Model Solution

13. The optimal solution for a linear programming problem will always occur at an extreme point.

Answer: True

Difficulty: Medium

Learning Objective: Calculate unused or surplus resources given a model solution and provide an overview of the simplex method.

Section Reference: S14.3 Linear Programming Model Solution

14. The simplex method used for solving linear programming problems uses matrix algebra to solve simultaneous equations.

Answer: True

Difficulty: Medium

Learning Objective: Calculate unused or surplus resources given a model solution and provide an overview of the simplex method.

Section Reference: S14.3 Linear Programming Model Solution

15. Because linear programming provides an optimal solution, sensitivity analysis is never an important consideration.

Answer: False

Difficulty: Medium

Learning Objective: Calculate unused or surplus resources given a model solution and provide an overview of the simplex method.

Section Reference: S14.3 Linear Programming Model Solution

MULTIPLE CHOICE QUESTIONS

16. ___ represent a restriction on decision variable values for a linear programming problem.

a) Surpluses

b) Constraints

c) Extreme points

d) Optimal points

Answer: b

Difficulty: Medium

Learning Objective: Formulate a basic linear programming model including the definition of decision variables, objective function, and constraints.

Section Reference: S14.1 Model Formulation

17. The simplex method is a solution method used for linear programming problems that have

a) no constraints.

b) at least one constraint.

c) at least two constraints.

d) at least three constraints.

Answer: a

Difficulty: Medium

Learning Objective: Formulate a basic linear programming model including the definition of decision variables, objective function, and constraints.

Section Reference: S14.1 Model Formulation

18. The area that contains the values that satisfies all the constraints in a linear programming problem is known as the ___ space.

a) optimal solution

b) non-optimal solution

c) feasible solution

d) infeasible solution

Answer: c

Difficulty: Medium

Learning Objective: Determine the optimal solution for a linear programming model with two decision variables using the graphical solution method.

Section Reference: S14.2 Graphical Solution Method

19. The optimal solution for a linear programming problem will always occur

a) when the slack price equals the surplus price.

b) when the surplus price equals the slack price.

c) at an extreme point.

d) at a non-extreme point.

Answer: c

Difficulty: Medium

Learning Objective: Determine the optimal solution for a linear programming model with two decision variables using the graphical solution method.

Section Reference: S14.2 Graphical Solution Method

20. The constraint 3x₁ + 6x₂ ≥ 48 is converted to an equality by

a) adding a slack variable.

b) subtracting a surplus variable.

c) adding both a slack variable and a surplus variable.

d) subtracting both a slack variable and a surplus variable.

Answer: b

Difficulty: Medium

Learning Objective: Calculate unused or surplus resources given a model solution and provide an overview of the simplex method.

Section Reference: S14.3 Linear Programming Model Solution

21. A company produces product A and product B. Each product must go through two processes. Each A produced requires two hours in process 1 and five hours in process 2. Each B produced requires six hours in process 1 and three hours in process 2. There are 80 hours of capacity available each week in each process. Each A produced generates $6.00 in profit for the company. Each B produced generates $9.00 in profit for the company. If the company produces 6 units of A and 9 units of B the company’s objective function is

a) $6.00A + $9.00B.

b) $9.00A + $6.00B.

c) $6.00A – $9.00B.

d) $6.00A*$9.00B.

Answer: a

Difficulty: Medium

Learning Objective: Calculate unused or surplus resources given a model solution and provide an overview of the simplex method.

Section Reference: S14.3 Linear Programming Model Solution

22. A company produces product A and product B. Each product must go through two processes. Each A produced requires two hours in process 1 and five hours in process 2. Each B produced requires six hours in process 1 and three hours in process 2. There are 80 hours of capacity available each week in each process. Each A produced generates $6.00 in profit for the company. Each B produced generates $9.00 in profit for the company. If the company produces 6 units of A and 9 units of B the constraint for process 1 is represented by

a) 2A + 5B ≤ 80.

b) 2A + 6B ≥ 80.

c) 2A + 6B < 80.

d) 2A + 6B ≤ 80.

Answer: d

Difficulty: Medium

Learning Objective: Calculate unused or surplus resources given a model solution and provide an overview of the simplex method.

Section Reference: S14.3 Linear Programming Model Solution

23. A company produces product A and product B. Each product must go through two processes. Each A produced requires two hours in process 1 and five hours in process 2. Each B produced requires six hours in process 1 and three hours in process 2. There are 80 hours of capacity available each week in each process. Each A produced generates $6.00 in profit for the company. Each B produced generates $9.00 in profit for the company. If the company produces 6 units of A and 9 units of B the capacity constraint for Process 2 is

a) 5A + 3B ≥ 80.

b) 6A + 3 B ≤ 80.

c) 5A + 3B ≤ 80.

d) 5A + 3B < 80.

Answer: c

Difficulty: Medium

Learning Objective: Calculate unused or surplus resources given a model solution and provide an overview of the simplex method.

Section Reference: S14.3 Linear Programming Model Solution

24. A company produces product A and product B. Each product must go through two processes. Each A produced requires two hours in process 1 and five hours in process 2. Each B produced requires six hours in process 1 and three hours in process 2. There are 80 hours of capacity available each week in each process. Each A produced generates $6.00 in profit for the company. Each B produced generates $9.00 in profit for the company. If the company produces 6 units of A and 9 units of B the value of the objective function is equal to

a) $36.

b) $81.

c) $108.

d) $117.

Answer: d

Difficulty: Medium

Learning Objective: Calculate unused or surplus resources given a model solution and provide an overview of the simplex method.

Section Reference: S14.3 Linear Programming Model Solution

25. A company produces product A and product B. Each product must go through two processes. Each A produced requires two hours in process 1 and five hours in process 2. Each B produced requires six hours in process 1 and three hours in process 2. There are 80 hours of capacity available each week in each process. Each A produced generates $6.00 in profit for the company. Each B produced generates $9.00 in profit for the company. If the company produces 6 units of A and 9 units of B the amount of slack (in hours) for process 1 is

a) 0 hours.

b) 14 hours.

c) 66 hours.

d) 80 hours.

Answer: a

Difficulty: Hard

Learning Objective: Calculate unused or surplus resources given a model solution and provide an overview of the simplex method.

Section Reference: S14.3 Linear Programming Model Solution

26. For a less than or equal to (≤) constraint, the shadow price represents the

a) amount you would be willing to pay for one additional unit of a resource.

b) amount you at which you would be willing to sell one additional unit of a resource.

c) difference between the slack price and the surplus price.

d) difference between the surplus price and the slack price.

Answer: a

Difficulty: Medium

Learning Objective: Interpret the sensitivity report from an Excel linear programming solution and perform sensitivity analysis.

Section Reference: S14.5 Sensitivity Analysis

SHORT-ANSWER ESSAY QUESTIONS

27. How is linear programming useful to an operations manager?

Answer: Linear programming is a mathematical modelling technique used to determine a level of operational activity in order to achieve an objective, subject to restrictions called constraints. Many decisions faced by an operations manager are centred around the best way to achieve the objectives of the firm subject to the constraints of the operating environment. There constraints can be limited resources, such as time, labour, energy, materials, or money, or they can be restrictive guidelines.

Difficulty: Medium

Learning Objective: Formulate a basic linear programming model including the definition of decision variables, objective function, and constraints.

Section Reference: S14.1 Model Formulation

28. Briefly define the components that comprise a linear programming model.

Answer: A linear programming model consists of decision variables, an objective function, and model constraints. Decision variables are mathematical symbols that represent levels of activity of an operation. The objective function is a linear mathematical relationship that describes the objective of an operation in terms of the decision variables. The model constraints are also linear relationships of the decision variables that represent the restrictions placed on the decision situation by the operating environment.

Difficulty: Medium

Learning Objective: Formulate a basic linear programming model including the definition of decision variables, objective function, and constraints.

Section Reference: S14.1 Model Formulation

29. What is meant by the term “shadow price” in linear programming?

Answer: The shadow prices are the marginal values (also referred to as dual values) of the resource constraints in the linear programming model. The shadow prices represent the amount the company would be willing to pay for one additional unit of a resource. The shadow prices are not the original selling prices of a resource, but are rather the amount the company should pay to get more of the resource. The shadow price is helpful to the company in pricing resources and making decisions about securing additional resources.

Difficulty: Medium

Learning Objective: Interpret the sensitivity report from an Excel linear programming solution and perform sensitivity analysis.

Section Reference: S14.5 Sensitivity Analysis

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