Table M7-3 -According to Table M7-3, which is the final simplex tableau for a linear programming problem (maximization), what would happen to profits if the X1 column were selected as the pivot column and another iteration of the simplex algorithm were performed?

A) Total profits would increase. B) Total profits would decrease. C) An infeasible solution would be found. D) Another optimal solution would be found. A) Total profits would increase. B) Total profits would decrease. C) An infeasible solution would be found. D) Another optimal solution would be found.

Table M7-1 -According to Table M7-1, it is currently profitable to produce some units of X1 and the current profit per unit of X1 is $20.What is the lowest value that this could be to allow this variable to remain in the basis?

A) 8 B) 16 C) 20 D) 30 A) 8 B) 16 C) 20 D) 30

The number -2 in the X2 column and X1 row of a simplex tableau implies that

A) if 1 unit of X2 is added to the solution, X1 will decrease by 2. B) if 1 unit of X1 is added to the solution, X2 will decrease by 2. C) if 1 unit of X2 is added to the solution, X1 will increase by 2. D) if 1 unit of X1 is added to the solution, X2 will increase by 2. A) if 1 unit of X2 is added to the solution, X1 will decrease by 2. B) if 1 unit of X1 is added to the solution, X2 will decrease by 2. C) if 1 unit of X2 is added to the solution, X1 will increase by 2. D) if 1 unit of X1 is added to the solution, X2 will increase by 2.

Exam 22: Linear Programming: The Simplex Method

An infeasible solution is indicated when all the C_j - Z_j row entries are of the proper sign to imply optimality, but an artificial variable remains in the solution.

(True/False)

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Question 81

In LP problems with more than two variables, the area of feasible solutions is known as an n-dimensional

(Multiple Choice)

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Question 82

The constraint 5X₁ + 6X₂ ≥ 30, when converted to an = constraint for use in the simplex algorithm, will be 5 X₁ + 6 X₂ - S = 30.

(True/False)

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Question 83

In applying the simplex solution procedure to a minimization problem to determine which variable enters the solution mix

(Multiple Choice)

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Question 84

Table M7-3 -According to Table M7-3, which is the final simplex tableau for a problem with two variables and two constraints, what is the maximum possible profit (objective function value)for this problem?

(Multiple Choice)

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Question 85

A minimization problem with two decision variables and three ≥ constraints can have two non-basic surplus variables.

(True/False)

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Question 86

The simplex method begins with an initial feasible solution in which all real variables are set equal to 0.

(True/False)

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Question 87

In a maximization problem, if a variable is to enter the solution, it must have a positive coefficient in the C_j - Z_j row.

(True/False)

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Question 88

Shadow prices are the positives of the numbers in the C_j - Z_j row's slack variable columns.

(True/False)

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Question 89

Convert the following linear program into a simplex model form. Maximize 8X + 10Y Subject to: 5X + 3Y ≤ 34 2X + 3Y = 22 X ≥ 3 X, Y ≥ 0

(Essay)

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Question 90

Table M7-3 -According to Table M7-3, which is the final simplex tableau for a linear programming problem (maximization), what would happen to profits if the X₁ column were selected as the pivot column and another iteration of the simplex algorithm were performed?

(Multiple Choice)

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Question 91

Consider the following linear programming problem: Maximize 40 X1 + 30 X2 + 60X3 Subject to: X1 + X2 + X3 ≥ 90 12 X1 + 8 X2 + 10 X3 ≤ 1500 X1 = 20 X3 ≤ 100 X1 , X2 , X3 ≥ 0 How many slack, surplus, and artificial variables would be necessary if the simplex algorithm were used to solve this problem?

(Multiple Choice)

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Question 92

The substitution rates

(Multiple Choice)

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Question 93

Table M7-1 -According to Table M7-1, it is currently profitable to produce some units of X₁ and the current profit per unit of X₁ is $20.What is the lowest value that this could be to allow this variable to remain in the basis?

(Multiple Choice)

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Question 94

The number -2 in the X₂ column and X₁ row of a simplex tableau implies that

(Multiple Choice)

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Question 95

In a maximization problem, if a variable is to enter the solution, it must have a negative coefficient in the C_j - Z_j row.

(True/False)

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Question 96

Karmarkar's algorithm reaches a solution quickly by compressing the edges of the feasible region.

(True/False)

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Question 97

The dual problem formulation can be solved using the same simplex process used for the primal formulation.

(True/False)

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Question 98

Showing 81 - 98 of 98

An infeasible solution is indicated when all the C_j - Z_j row entries are of the proper sign to imply optimality, but an artificial variable remains in the solution.

In LP problems with more than two variables, the area of feasible solutions is known as an n-dimensional

The constraint 5X₁ + 6X₂ ≥ 30, when converted to an = constraint for use in the simplex algorithm, will be 5 X₁ + 6 X₂ - S = 30.

In applying the simplex solution procedure to a minimization problem to determine which variable enters the solution mix

Table M7-3 -According to Table M7-3, which is the final simplex tableau for a problem with two variables and two constraints, what is the maximum possible profit (objective function value)for this problem?

A minimization problem with two decision variables and three ≥ constraints can have two non-basic surplus variables.

The simplex method begins with an initial feasible solution in which all real variables are set equal to 0.

In a maximization problem, if a variable is to enter the solution, it must have a positive coefficient in the C_j - Z_j row.

Shadow prices are the positives of the numbers in the C_j - Z_j row's slack variable columns.

Convert the following linear program into a simplex model form. Maximize 8X + 10Y Subject to: 5X + 3Y ≤ 34 2X + 3Y = 22 X ≥ 3 X, Y ≥ 0

Table M7-3 -According to Table M7-3, which is the final simplex tableau for a linear programming problem (maximization), what would happen to profits if the X₁ column were selected as the pivot column and another iteration of the simplex algorithm were performed?

The substitution rates

Table M7-1 -According to Table M7-1, it is currently profitable to produce some units of X₁ and the current profit per unit of X₁ is $20.What is the lowest value that this could be to allow this variable to remain in the basis?

The number -2 in the X₂ column and X₁ row of a simplex tableau implies that

In a maximization problem, if a variable is to enter the solution, it must have a negative coefficient in the C_j - Z_j row.

Karmarkar's algorithm reaches a solution quickly by compressing the edges of the feasible region.

The dual problem formulation can be solved using the same simplex process used for the primal formulation.

Introduction to Quantitative Analysis

Probability Concepts and Applications

Decision Analysis

Regression Models

Forecasting

Inventory Control Models

Linear Programming Models: Graphical and Computer Methods

Linear Programming Applications

Transportation, Assignment, and Network Models

Integer Programming, Goal Programming, and Nonlinear Programming

Project Management

Waiting Lines and Queuing Theory Models

Simulation Modeling

Markov Analysis

Statistical Quality Control

Analytic Hierarchy Process

Dynamic Programming

Decision Theory and the Normal Distribution

Game Theory

Mathematical Tools: Determinants and Matrices

Calculus-Based Optimization

Transportation, Assignment, and Network Algorithms

Filters

Exam 22: Linear Programming: The Simplex Method

An infeasible solution is indicated when all the Cj - Zj row entries are of the proper sign to imply optimality, but an artificial variable remains in the solution.

In LP problems with more than two variables, the area of feasible solutions is known as an n-dimensional

The constraint 5X1 + 6X2 ≥ 30, when converted to an = constraint for use in the simplex algorithm, will be 5 X1 + 6 X2 - S = 30.

In applying the simplex solution procedure to a minimization problem to determine which variable enters the solution mix

Table M7-3 -According to Table M7-3, which is the final simplex tableau for a problem with two variables and two constraints, what is the maximum possible profit (objective function value)for this problem?

A minimization problem with two decision variables and three ≥ constraints can have two non-basic surplus variables.

The simplex method begins with an initial feasible solution in which all real variables are set equal to 0.

In a maximization problem, if a variable is to enter the solution, it must have a positive coefficient in the Cj - Zj row.

Shadow prices are the positives of the numbers in the Cj - Zj row's slack variable columns.

Convert the following linear program into a simplex model form. Maximize 8X + 10Y Subject to: 5X + 3Y ≤ 34 2X + 3Y = 22 X ≥ 3 X, Y ≥ 0

Table M7-3 -According to Table M7-3, which is the final simplex tableau for a linear programming problem (maximization), what would happen to profits if the X1 column were selected as the pivot column and another iteration of the simplex algorithm were performed?

The substitution rates

Table M7-1 -According to Table M7-1, it is currently profitable to produce some units of X1 and the current profit per unit of X1 is $20.What is the lowest value that this could be to allow this variable to remain in the basis?

The number -2 in the X2 column and X1 row of a simplex tableau implies that

In a maximization problem, if a variable is to enter the solution, it must have a negative coefficient in the Cj - Zj row.

Karmarkar's algorithm reaches a solution quickly by compressing the edges of the feasible region.

The dual problem formulation can be solved using the same simplex process used for the primal formulation.

Introduction to Quantitative Analysis

Probability Concepts and Applications

Decision Analysis

Regression Models

Forecasting

Inventory Control Models

Linear Programming Models: Graphical and Computer Methods

Linear Programming Applications

Transportation, Assignment, and Network Models

Integer Programming, Goal Programming, and Nonlinear Programming

Project Management

Waiting Lines and Queuing Theory Models

Simulation Modeling

Markov Analysis

Statistical Quality Control

Analytic Hierarchy Process

Dynamic Programming

Decision Theory and the Normal Distribution

Game Theory

Mathematical Tools: Determinants and Matrices

Calculus-Based Optimization

Transportation, Assignment, and Network Algorithms

Filters

An infeasible solution is indicated when all the C_j - Z_j row entries are of the proper sign to imply optimality, but an artificial variable remains in the solution.

The constraint 5X₁ + 6X₂ ≥ 30, when converted to an = constraint for use in the simplex algorithm, will be 5 X₁ + 6 X₂ - S = 30.

In a maximization problem, if a variable is to enter the solution, it must have a positive coefficient in the C_j - Z_j row.

Shadow prices are the positives of the numbers in the C_j - Z_j row's slack variable columns.

Table M7-3 -According to Table M7-3, which is the final simplex tableau for a linear programming problem (maximization), what would happen to profits if the X₁ column were selected as the pivot column and another iteration of the simplex algorithm were performed?

Table M7-1 -According to Table M7-1, it is currently profitable to produce some units of X₁ and the current profit per unit of X₁ is $20.What is the lowest value that this could be to allow this variable to remain in the basis?

The number -2 in the X₂ column and X₁ row of a simplex tableau implies that

In a maximization problem, if a variable is to enter the solution, it must have a negative coefficient in the C_j - Z_j row.