CHAPTER 1
1. The field of management science approaches decision making rationally, with techniques
based on the scientific method. TRUE
2. A model that uses a system of symbols to represent a problem is called mathematical
model. TRUE
3. The value of any model is that it enables the user to make inferences about the real
situation. TRUE
4. The first step in problem solving is the definition of decision variables. FALSE
5. The process of decision making is more limited than that of problem solving. TRUE
6. The most successful quantitative analysis will separate the analyst from the managerial
team until after the problem is fully structured. FALSE
7. Problem solving encompasses both the identification of a problem and the action to resolve
it. TRUE
8. The first step in the decision making process is to identify the problem. TRUE
9. When the value of the output cannot be determined even if the value of the controllable
input is known, the model is stochastic. TRUE
10. The feasible solution is the best solution possible for a mathematical model. FALSE
11. Uncontrollable inputs are the decision variables for a model. FALSE
12. Management Science, Business Analytics, & Operations Research are commonly used
names for the body of knowledge involving quantitative approaches to decision-making?
TRUE
13. The decision making process includes implementation and evaluation of the decision.
FALSE
14. In quantitative analysis, the optimal solution is the mathematically-best solution. TRUE
15. The terms 'stochastic' and 'deterministic' have the same meaning in quantitative analysis.
FALSE
16. Inputs to quantitative model must all be deterministic id the problem is to have a solution.
FALSE
17. All uncontrollable inputs or data must be specified before we can analyze the model and
recommend a decision or solution for the problem. TRUE
18. Model development should be left to the quantitative analysts; the model user’s involvement
should begin at the implementation stage. FALSE
19. Identification and definition of a problem is the final step of problem solving. FALSE
20. Problem definition must occur prior to the quantitative analysis process. TRUE
21. The value of any model is that it enables the user to make inferences about the situation.
TRUE
22. The quantitative analysis approach requires the manager’s prior experience with a similar
problem. FALSE
23. The volume that results in marginal revenue equaling the marginal cost is called the breakeven point. FALSE
24. Frederick Taylor is credited with forming the first MS/OR interdisciplinary teams in the 1940s
FALSE.
25. A company seeks to maximize profit subject to limited availability man-hours. Man-hours is a
controllable input. FALSE
26. To find the choice that provides the highest profit and the fewest employees, apply a singlecriterion decision process. FALSE
27. George Dantzig is important in the history if management science because he developed
the simplex method for linear programming. TRUE
28. A toy train layout designed to represent an actual railyard is an example of an analog model.
FALSE
29. The most critical component in determining the success or failure of any quantitative
approach to decision making is problem definition. TRUE
30. A physical model that does not have the same physical appearance as the object being
modeled is analog model. TRUE
CHAPTER 2 & 3
1. In a given mathematical model, Max. CM = 10A + 15B is a constraint function. FALSE
2. Relevant costs should be reflected in the objective function, but sunk costs should not.
TRUE
3. Linear programming is a mathematical technique used to maximized a revenue,
contribution margin, or profit, or minimize a cost function subject to constraints, such as
scarce resources and production capacity. TRUE
4. Because the dual price represents the improvement in the value of the optimal solution per
unit increase in right-hand-side, a dual price cannot be negative. FALSE
5. Decreasing the objective function coefficient of a variable to its lower limit will create a
revised problem that is unbounded. FALSE
6. The constraint 2x1 − x2 = 0 passes through the point (200,100). FALSE
7. In linear programming, sensitivity analysis is used to develop the optimal solution to the
problem. FALSE
8. Any change to the objective function coefficient of a variable that is positive in the optimal
solution will change the optimal solution. FALSE
9. Decision variables limit the degree to which the objective in a linear programming problem
is satisfied. FALSE
10. The 100% Rule does not imply that the optimal solution will necessarily change if the
percentage exceeds 100%. TRUE
11. In an LP problem, at least one corner point must be an optimal solution if an optimal
solution exists. TRUE
12. Increasing the objective function coefficient in a maximization problem would cause a
change in the feasible region. FALSE
13. A range of optimality is applicable only if the other coefficient remains at its original value.
TRUE
14. In LP, variables do not have to be integer valued and may take on any fractional
value. This assumption is called divisibility. TRUE
15. Alternative optimal solutions occur when there is no feasible solution to the problem.
FALSE
16. All of the following statements about a redundant constraint are correct EXCEPT (D)
A.
B.
C.
D.
A redundant constraint does not affect the optimal solution.
A redundant constraint does not affect the feasible region.
Recognizing a redundant constraint is easy with the graphical solution method.
At the optimal solution, a redundant constraint will have zero slack.
17. The amount the objective function coefficient of a decision variable would have to improve
before that variable would have a positive value in the solution is the REDUCED COST
18. Which of the following would cause a change in the feasible region? (D)
A.
B.
C.
D.
Adding a redundant constraint
Increasing an objective function coefficient in a maximization problem
Increasing an objective function coefficient in a minimization problem.
Changing the right-hand side of a non-redundant constraint
19. The cost that varies depending on the values of the decision variables is a RELEVANT
COST
20. To find the optimal solution to a linear programming problem using the graphical method
(C)
A. Find the feasible point that is closest to the origin.
B. Find the feasible point that is the farthest away from the origin.
C. None of the alternatives is correct.
D. find the feasible point that is at the highest location.
21. The 100% Rule compares (C)
A.
B.
C.
D.
dual prices to reduced cost
New values to original values
Proposed changes to allowed changes
Objective function changes to right-hand side changes
22. Linear programming problems can be solved using either the graphical method or the
simplex method. Which of the following statements about the graphical method is not
correct? (A)
A. The graphical method is limited to situations having two restrictions (constraints)
B. The graphic solution depicts the area of feasible combinations of activity given the
constraints.
C. The graph depicts the optimal corner point.
D. The graphic method can be used given more than two restrictions
23. All linear programming problems have all of the following properties EXCEPT (D)
A. A linear objective function that is to be maximized or minimized.
B. Variables that are all restricted to nonnegative values.
C. A set of linear constraints.
D. Alternative optimal solutions.
24. Decision variables (C)
A. Represent the values of the constraints.
B. Measure the objective function
C. Must exist for each constraint.
D. Tell how much or how many of something to produce, invest, purchase, hire, etc.
25. When using a graphical solution procedure, the region bounded by the set of constraint is
called FEASIBLE REGION
26. Which of the following special cases does not require reformulation of the problem in order
to obtain a solution? ALTERNATE OPTIMALITY
27. A redundant constraint results in NO CHANGE IN THE OPTIMAL SOLUTION
28. In LP, variables do not have to be integer valued and may take on any fractional value.
This assumption is called DIVISIBILITY
29. In solving a linear program the condition of infeasibility occurred. To resolve this problem
we might add another constraint. FALSE
30. If the feasible region gets larger due to the change in one of the constraints the optimal
value of the objective function must increase or remain the same for a maximization
problem. TRUE
31. When alternate optimal solutions exist in an LP problem then the two constraints would be
parallel. FALSE
32. When alternate optimal solutions exist in an LP problem then the objective function will be
parallel to one of the constraints. TRUE
33. In a linear programming model, the constraints are the scarce resources. TRUE
34. No matter what value it has, each objective function line is parallel to every other objective
function in a problem. TRUE
35. A solution that satisfies all the constraints of a linear programming problem except the
non-negativity constraint is called INFEASIBLE
36. A linear program has been solved and sensitivity analysis has been performed. The
ranges for the objective function coefficients have been found. for the profit on X1, the
upper bound is 80, the lower bound is 60, and the current value is 75. Which of the
following must be true if the profit on this variable is lowered to 70 and the optimal solution
is found? (B)
a. A new corner point will become optimal
b. The values for all the decision variables will remain the same
c. The maximum possible total profit may increase
d. All of the above is possible
37. A linear programming problem that has a bounded feasible region. If this problem has an
equality (=) constraint, then THE FEASIBLE REGION MUST CONTAIN A LINE
SEGMENT
38. A redundant constraint is a binding constraint. FALSE
39. An optimal solution to a LP problem can be found at the extreme point of the feasible
region for the problem. TRUE
40. In an LP problem at least one corner point must be an optimal solution id an optimal
solution exists. TRUE
41. A linear programming problem that has a bounded feasible region. If this problem has an
equality (=) constraint, then the feasible region must contain a line segment. TRUE
42. The amount that the objective function coefficient of a decision variable would have to
improve before that variable would have a positive value in the solution is the REDUCED
COST
43. A constraint that does not affect the feasible region is a REDUNDANT CONSTRAINT
44. The feasible solution is the best solution possible for a mathematical model. FALSE
45. Decision alternatives should be identified before the decision criteria are established.
TRUE
46. Only the binding constraints form the shape (boundaries) of the feasible region. FALSE
47. All of the following statements about a redundant constraint are correct EXCEPT (A)
a. At the optimal solution a redundant constraint will have zero slack.
b. A redundant constraint does not affect the optimal solution.
c. Recognizing a redundant constraint is easy with the graphical method solution.
d. A redundant constraint does not affect the feasible region.
48. A graphical method should only be used to solve a LP problem when THERE ARE ONLY
TWO CONSTRAINTS
49. As long as the slope of the objective function stay between the slopes of the binding
constraints THE VALUES OF THE DUAL VARIABLES WON’T CHANGE.
50. The maximization or minimization of a quantity is the OBJECTIVE OF LINEAR
PROGRAMMING
51. If the range of feasibility indicates that the original amount of a resource which was 20 can
increase by 5 then the amount of resource can increase to 25. TRUE
52. An alternative optimal solution occurs when there is no feasible solution to the problem.
FALSE
53. The standard form of a linear programming problem will have the same solution as the
original problem. TRUE
54. In the optimal solution to a linear program, there are 20 units slack for a constraint. From
this we know: THE DUAL CONSTRAINT IS 0
55. Because surplus variables represent the amount by which the solution exceeds a
minimum target they are given positive coefficients in the objective function. FALSE
56. It is possible to have exactly two optimal solutions to a linear programming problem.
FALSE
57. An unbounded feasible region might not result in an unbounded solution for a minimization
or maximization problem. TRUE
58. In a feasible problem an equal to constraint cannot be nonbinding. TRUE
59. When using a graphical solution procedure, the region bounded by the set of constraints s
called the feasible region. TRUE
60. In solving linear program the condition of infeasibility occurred. To resolve this problem we
might: REMOVE OR RELAX A CONSTRAINT
61. To solve a LP slack surplus and artificial variables must be employed. Which of the
following statement s about a slack variable is correct? (C)
a. It is the benefit foregone by using scarce resource in a given way
b. Its total amount varies with the change in cost driver but its cost per driver is constant
within the relevant range
c. It represents unused capacity and is added to inequalities of the type to convert them
into inequalities
d. It refers to the benefit of moving the feasible area
62. Which of the following is a valid objective function for a linear programming problem?
Min 4x + 3y + (2/3z)
63. A feasible solution to a linear programming problem: MUST SATISFY ALL OF THE
PROBLEM’S CONSTRAINTS SIMULTANEOUSLY
64. In solving a linear program the condition of infeasibility occurred. To resolve the problem
we might remove or relax the constraint. TRUE
65. If there is a maximum of 4000 hours of labor available per month and the 300 ping-pong
balls (𝑥1 ) or 125 wiffle balls (𝑥2 ) can be produced per hour of labor which of the following
constraints reflect this solution? 300x1 + 125x2 < 4000
66. Increasing the right hand side of a nonbinding constraint will not cause a change in the
optimal solution. FALSE
67. If the feasible region gets larger due to the change in one of the constraints the optimal
value of the objective function must increase or remain the same for a minimization
problem. FALSE