Question 1

Consider the following linear programming problem
Max
8X + 7Y
s.t.
15X + 5Y ≤ 75
10X + 6Y ≤ 60
X + Y ≤ 8
X, Y ≥ 0
​
a.Use a graph to show each constraint and the feasible region.
b.Identify the optimal solution point on your graph. What are the values of X and Y at the optimal solution?
c.What is the optimal value of the objective function?

Accepted Answer

a. <img  loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> B.The optimal solution occ...

Question 2

No matter what value it has, each objective function line is parallel to every other objective function line in a problem.

Accepted Answer

A) True 
 B)False

Question 3

All of the following statements about a redundant constraint are correct EXCEPT

Accepted Answer

A)   A redundant constraint does not affect the optimal solution.
B)   A redundant constraint does not affect the feasible region.
C)   Recognizing a redundant constraint is easy with the graphical solution method.
D)   At the optimal solution, a redundant constraint will have zero slack.E) All of the above
F) None of the above

Question 4

An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

Accepted Answer

A) True 
 B)False

Question 5

The point (3, 2) is feasible for the constraint 2x1 + 6x2 ≤ 30.

Accepted Answer

A) True 
 B)False

Question 6

Find the complete optimal solution to this linear programming problem.
Min
3X + 3Y
s.t.
12X + 4Y ≥ 48
10X + 5Y ≥ 50
4X + 8Y ≥ 32
X , Y ≥ 0

Accepted Answer

The complete optimal solution is X = 4, Y = 2, Z = 18, S₁ = 8, S₂ = 0, S₃ = 0

Question 7

Decision variables

Accepted Answer

A)   tell how much or how many of something to produce, invest, purchase, hire, etc.
B)   represent the values of the constraints.
C)   measure the objective function.
D)   must exist for each constraint.E) All of the above
F) C) and D)

Question 8

Which of the following special cases does not require reformulation of the problem in order to obtain a solution?

Accepted Answer

A)   alternate optimality
B)   infeasibility
C)   unboundedness
D)   each case requires a reformulation.E) All of the above
F) None of the above

Question 9

The improvement in the value of the objective function per unit increase in a right-hand side is the

Accepted Answer

A)   sensitivity value.
B)   dual price.
C)   constraint coefficient.
D)   slack value.E) C) and D)
F) A) and C)

Question 10

To find the optimal solution to a linear programming problem using the graphical method

Accepted Answer

A)   find the feasible point that is the farthest away from the origin.
B)   find the feasible point that is at the highest location.
C)   find the feasible point that is closest to the origin.
D)   None of the alternatives is correct.E) None of the above
F) A) and B)

Question 11

All linear programming problems have all of the following properties EXCEPT

Accepted Answer

A)   a linear objective function that is to be maximized or minimized.
B)   a set of linear constraints.
C)   alternative optimal solutions.
D)   variables that are all restricted to nonnegative values.E) B) and C)
F) None of the above

Question 12

A range of optimality is applicable only if the other coefficient remains at its original value.

Accepted Answer

A) True 
 B)False

Question 13

Which of the following statements is NOT true?

Accepted Answer

A)   A feasible solution satisfies all constraints.
B)   An optimal solution satisfies all constraints.
C)   An infeasible solution violates all constraints.
D)   A feasible solution point does not have to lie on the boundary of the feasible region.E) B) and C)
F) A) and D)

Question 14

In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables.

Accepted Answer

A) True 
 B)False

Question 15

Decision variables limit the degree to which the objective in a linear programming problem is satisfied.

Accepted Answer

A) True 
 B)False

Question 16

Which of the following is a valid objective function for a linear programming problem?

Accepted Answer

A)   Max 5xy
B)   Min 4x + 3y + (2/3) z
C)   Max 5x2 + 6y2
D)   Min (x1 + x2) /x3E) A) and B)
F) A) and C)

Question 17

As long as the slope of the objective function stays between the slopes of the binding constraints

Accepted Answer

A)   the value of the objective function won't change.
B)   there will be alternative optimal solutions.
C)   the values of the dual variables won't change.
D)   there will be no slack in the solution.E) B) and C)
F) B) and D) C

Question 18

Does the following linear programming problem exhibit infeasibility, unboundedness, or alternate optimal solutions? Explain.
Min
3X + 3Y
s.t.
1X + 2Y ≤ 16
1X + 1Y ≤ 10
5X + 3Y ≤ 45
X , Y ≥ 0

Accepted Answer

The proble...

Question 19

The maximization or minimization of a quantity is the

Accepted Answer

A)   goal of management science.
B)   decision for decision analysis.
C)   constraint of operations research.
D)   objective of linear programming.E) B) and C)
F) B) and D)

Question 20

Consider the following linear program:
Max
60X + 43Y
s.t.
X + 3Y ≥ 9
6X − 2Y = 12
X + 2Y ≤ 10
X, Y ≥ 0
​
a.
Write the problem in standard form.
b.
What is the feasible region for the problem?
c.
Show that regardless of the values of the actual objective function coefficients, the optimal solution will occur at one of two points. Solve for these points and then determine which one maximizes the current objective function.

Accepted Answer

a.Max 60X + 43Y s.t. X + 3Y − S₁ = 9 6X − 2Y = 12 X + 2Y + S₃ = 10 X, Y, S₁, S₃ ≥ 0 B.Line segment of 6X − 2Y = 12 between (22/7,24/7) and (27/10,21/10). C.Extreme points: (22/7,24/7) and (27/10,21/10). First one is optimal, giving Z = 336.

Exam 2: An Introduction to Linear Programming

Correct Answer
verified
a. B.The optimal solution occ...
View Answer

No matter what value it has, each objective function line is parallel to every other objective function line in a problem.

Correct Answer
verified

All of the following statements about a redundant constraint are correct EXCEPT

Correct Answer
verified

An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

Correct Answer
verified

The point (3, 2) is feasible for the constraint 2x₁ + 6x₂ ≤ 30.

Correct Answer
verified

Find the complete optimal solution to this linear programming problem. Min 3X + 3Y s.t. 12X + 4Y ≥ 48 10X + 5Y ≥ 50 4X + 8Y ≥ 32 X , Y ≥ 0

Correct Answer
verified
11eb1774_5184_e11e_931a_55ceeec7188f_TB6979_00 The complete optimal solution is X = 4, Y = 2, Z = 18, S₁ = 8, S₂ = 0, S₃ = 0

Decision variables

Correct Answer
verified

Which of the following special cases does not require reformulation of the problem in order to obtain a solution?

Correct Answer
verified

The improvement in the value of the objective function per unit increase in a right-hand side is the

Correct Answer
verified

To find the optimal solution to a linear programming problem using the graphical method

Correct Answer
verified

All linear programming problems have all of the following properties EXCEPT

Correct Answer
verified

A range of optimality is applicable only if the other coefficient remains at its original value.

Correct Answer
verified

Which of the following statements is NOT true?

Correct Answer
verified

In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables.

Correct Answer
verified

Decision variables limit the degree to which the objective in a linear programming problem is satisfied.

Correct Answer
verified

Which of the following is a valid objective function for a linear programming problem?

Correct Answer
verified

As long as the slope of the objective function stays between the slopes of the binding constraints

Correct Answer
verified
C

Does the following linear programming problem exhibit infeasibility, unboundedness, or alternate optimal solutions? Explain. Min 3X + 3Y s.t. 1X + 2Y ≤ 16 1X + 1Y ≤ 10 5X + 3Y ≤ 45 X , Y ≥ 0

Correct Answer
verified
The proble...
View Answer

The maximization or minimization of a quantity is the

Correct Answer
verified

Correct Answer
verified
a.Max 60X + 43Y s.t. X + 3Y − S₁ = 9 6X − 2Y = 12 X + 2Y + S₃ = 10 X, Y, S₁, S₃ ≥ 0 B.Line segment of 6X − 2Y = 12 between (22/7,24/7) and (27/10,21/10). C.Extreme points: (22/7,24/7) and (27/10,21/10). First one is optimal, giving Z = 336.

Exam 2: An Introduction to Linear Programming

Correct Answerverifieda. B.The optimal solution occ...View AnswerShow Answer

No matter what value it has, each objective function line is parallel to every other objective function line in a problem.

Correct AnswerverifiedShow Answer

All of the following statements about a redundant constraint are correct EXCEPT

Correct AnswerverifiedShow Answer

An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

Correct AnswerverifiedShow Answer

The point (3, 2) is feasible for the constraint 2x1 + 6x2 ≤ 30.

Correct AnswerverifiedShow Answer

Find the complete optimal solution to this linear programming problem. Min 3X + 3Y s.t. 12X + 4Y ≥ 48 10X + 5Y ≥ 50 4X + 8Y ≥ 32 X , Y ≥ 0

Correct Answerverified​ 11eb1774_5184_e11e_931a_55ceeec7188f_TB6979_00 ​ The complete optimal solution is X = 4, Y = 2, Z = 18, S1 = 8, S2 = 0, S3 = 0

Decision variables

Correct AnswerverifiedShow Answer

Which of the following special cases does not require reformulation of the problem in order to obtain a solution?

Correct AnswerverifiedShow Answer

The improvement in the value of the objective function per unit increase in a right-hand side is the

Correct AnswerverifiedShow Answer

To find the optimal solution to a linear programming problem using the graphical method

Correct AnswerverifiedShow Answer

All linear programming problems have all of the following properties EXCEPT

Correct AnswerverifiedShow Answer

A range of optimality is applicable only if the other coefficient remains at its original value.

Correct AnswerverifiedShow Answer

Which of the following statements is NOT true?

Correct AnswerverifiedShow Answer

In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables.

Correct AnswerverifiedShow Answer

Decision variables limit the degree to which the objective in a linear programming problem is satisfied.

Correct AnswerverifiedShow Answer

Which of the following is a valid objective function for a linear programming problem?

Correct AnswerverifiedShow Answer

As long as the slope of the objective function stays between the slopes of the binding constraints

Correct AnswerverifiedC

Does the following linear programming problem exhibit infeasibility, unboundedness, or alternate optimal solutions? Explain. Min 3X + 3Y s.t. 1X + 2Y ≤ 16 1X + 1Y ≤ 10 5X + 3Y ≤ 45 X , Y ≥ 0

Correct AnswerverifiedThe proble...View AnswerShow Answer

The maximization or minimization of a quantity is the

Correct AnswerverifiedShow Answer

Correct Answerverified​ a.Max 60X + 43Y s.t. X + 3Y − S1 = 9 6X − 2Y = 12 X + 2Y + S3 = 10 X, Y, S1, S3 ≥ 0 B.Line segment of 6X − 2Y = 12 between (22/7,24/7) and (27/10,21/10). C.Extreme points: (22/7,24/7) and (27/10,21/10). First one is optimal, giving Z = 336.

Correct Answer
verified
a. B.The optimal solution occ...
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Correct Answer
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Correct Answer
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The point (3, 2) is feasible for the constraint 2x₁ + 6x₂ ≤ 30.

Correct Answer
verified

Correct Answer
verified
11eb1774_5184_e11e_931a_55ceeec7188f_TB6979_00 The complete optimal solution is X = 4, Y = 2, Z = 18, S₁ = 8, S₂ = 0, S₃ = 0

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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C

Correct Answer
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The proble...
View Answer

Correct Answer
verified

Correct Answer
verified
a.Max 60X + 43Y s.t. X + 3Y − S₁ = 9 6X − 2Y = 12 X + 2Y + S₃ = 10 X, Y, S₁, S₃ ≥ 0 B.Line segment of 6X − 2Y = 12 between (22/7,24/7) and (27/10,21/10). C.Extreme points: (22/7,24/7) and (27/10,21/10). First one is optimal, giving Z = 336.