Exam 22: Linear Programming: The Simplex Method

If, at an optimal solution, the C_j - Z_j value for a real variable that is not in the solution mix has a value of one, there are multiple optimal solutions.

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(True/False)

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Question 1

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What are the five steps of the simplex method for maximization problems?

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Question 2

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1.Determine which variable to enter into the solution mix next. 2.Determine which variable to replace. 3.Compute new values for the pivot row. 4.Compute the new values for each remaining row. 5.Compute the Zj and Cj - Zj rows.Iterate to step 1 as required.

Sensitivity analyses are used to examine the effects of changes in

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Question 3

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Which of the following is true about surplus variables in a simplex tableau?

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Question 4

Nonbasic variables in the simplex method of linear programming are

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Question 5

The dual of a maximization problem with three decision variables and two constraints will be a maximization problem with only two decision variables in the objective function.

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Question 6

A surplus variable is added to a constraint in order to create an equality, and represents a quantity of unused resource.

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Question 7

Basic variables may be in the solution mix or out of the solution mix, just not at the same time.

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Question 8

Right-hand side ranging

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Question 9

Explain what an artificial variable represents in a constraint.

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Question 10

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

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Question 11

Write the dual of the following linear program. Minimize Z = 12 X1 + 30 X2 Subject to: 32 X1 + 18 X2 ≥ 600 24 X1 + 48 X2 ≥ 800 X1, X2 ≥ 0

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Question 12

Shadow prices represent

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Question 13

Which of the following is not true of artificial variables?

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Question 14

A basic feasible solution is a solution to a linear programming problem that corresponds to a corner point of the feasible region.

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Question 15

Table M7-1 -According to Table M7-1, all of the resources are being used.If the amount of resource B were changed from 96 to 97, then the maximum possible total profit would be

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Question 16

If all the numbers in the pivot column are negative, this implies that the solution is unbounded.

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Question 17

A surplus variable is added to an = constraint in order to utilize the simplex algorithm.

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Question 18

The dual of a primal minimization problem with two decision variables and three constraints will be a maximization problem with three decision variables in the objective function.

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Question 19

The following is a partial simplex tableau for a maximization problem after one iteration.Fill out the rest of this tableau, and then develop the next simplex tableau.

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Question 20

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Exam 22: Linear Programming: The Simplex Method

If, at an optimal solution, the Cj - Zj value for a real variable that is not in the solution mix has a value of one, there are multiple optimal solutions.

What are the five steps of the simplex method for maximization problems?

Sensitivity analyses are used to examine the effects of changes in

Which of the following is true about surplus variables in a simplex tableau?

Nonbasic variables in the simplex method of linear programming are

The dual of a maximization problem with three decision variables and two constraints will be a maximization problem with only two decision variables in the objective function.

A surplus variable is added to a constraint in order to create an equality, and represents a quantity of unused resource.

Basic variables may be in the solution mix or out of the solution mix, just not at the same time.

Right-hand side ranging

Explain what an artificial variable represents in a constraint.

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

Write the dual of the following linear program. Minimize Z = 12 X1 + 30 X2 Subject to: 32 X1 + 18 X2 ≥ 600 24 X1 + 48 X2 ≥ 800 X1, X2 ≥ 0

Shadow prices represent

Which of the following is not true of artificial variables?

A basic feasible solution is a solution to a linear programming problem that corresponds to a corner point of the feasible region.

Table M7-1 -According to Table M7-1, all of the resources are being used.If the amount of resource B were changed from 96 to 97, then the maximum possible total profit would be

If all the numbers in the pivot column are negative, this implies that the solution is unbounded.

A surplus variable is added to an = constraint in order to utilize the simplex algorithm.

The dual of a primal minimization problem with two decision variables and three constraints will be a maximization problem with three decision variables in the objective function.

The following is a partial simplex tableau for a maximization problem after one iteration.Fill out the rest of this tableau, and then develop the next simplex tableau.

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

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If, at an optimal solution, the C_j - Z_j value for a real variable that is not in the solution mix has a value of one, there are multiple optimal solutions.

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