Write the following problem in tableau form. Which variables would be in the initial basis? Max x1 + 2x2 s.t. 3x1 + 4x2 $\le$100 2x1 + 3.5x2 $\ge$ 60 2x1 -1x2 = 4 x1 , x2 $\ge$ 0

Max x 1 + 2x 2 -Ma 1 -Ma 2 s.t.3x 1 + 4x

Exam 17: Linear Programming: Simplex Method

Write the following problem in tableau form. Which variables would be in the initial basic solution? Min Z = 3x₁ + 8x₂ s.t. x₁ + x₂ $\le$ 200 x₁ $\le$ 80 x₂ $\le$ 60

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Question 1

Correct Answer:

Verified

Min Z
= 3x₁ + 8x₂ + Ma₁ + Ma₂
s.t.x₁ + x₂+ a₁ = 200
x₁ + s₁ = 80
x₂ + s₂+ a₂ = 60
The initial basis includes a₁, a₂, and s₂.

Artificial variables are added for the purpose of obtaining an initial basic feasible solution.

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(True/False)

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Question 2

Correct Answer:

Verified

True

The variable to enter into the basis is the variable with the largest positive c_j - z_j value.

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(True/False)

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Question 3

Correct Answer:

Verified

True

When there is a tie between two or more variables for removal from the simplex tableau,

(Multiple Choice)

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Question 4

When a set of simultaneous equations has more variables than constraints,

(Multiple Choice)

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Question 5

What is an artificial variable? Why is it necessary?

(Short Answer)

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Question 6

The variable to remove from the current basis is the variable with the smallest positive c_j - z_j value.

(True/False)

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Question 7

Comment on the solution shown in this simplex tableau. Basis 3 5 9 0 0 9 1/3 2/3 1 1/3 0 40 0 5/3 19/3 0 -1/3 1 100 3 6 9 3 0 360 - 0 -1 0 -3 0

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Question 8

Every extreme point of the graph of a two variable linear programming problem is a basic feasible solution.

(True/False)

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Question 9

Coefficients in a nonbasic column in a simplex tableau indicate the amount of decrease in the current basic variables when the value of the nonbasic variable is increased from 0 to 1.

(True/False)

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Question 10

The basic solution to a problem with three equations and four variables would assign a value of 0 to

(Multiple Choice)

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Question 11

A solution is optimal when all values in the c_j -z_j row of the simplex tableau are either zero or positive.

(True/False)

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Question 12

Comment on the solution shown in this simplex tableau. Basis 4 6 5 0 0 0 3 0 -1 1 -1 26 6 1 1 1 0 -1 10 6 6 6 0 -6 60 - -2 0 -1 0 6

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Question 13

To determine a basic solution set of n-m, the variables equal to zero and solve the m linear constraint equations for the remaining m variables.

(True/False)

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Question 14

In the simplex method, a tableau is optimal only if all the c_j -z_j values are

(Multiple Choice)

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Question 15

When a system of simultaneous equations has more variables than equations, there is a unique solution.

(True/False)

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Question 16

What coefficient is assigned to an artificial variable in the objective function?

(Multiple Choice)

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Question 17

Write the following problem in tableau form. Which variables would be in the initial basis? Max x₁ + 2x₂ s.t. 3x₁ + 4x₂ $\le$ 100 2x₁ + 3.5x₂ $\ge$ 60 2x₁ -1x₂ = 4 x₁ , x₂ $\ge$ 0

(Essay)

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Question 18

A basic solution and a basic feasible solution

(Multiple Choice)

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Question 19

The purpose of the tableau form is to provide

(Multiple Choice)

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Question 20

Exam 17: Linear Programming: Simplex Method

Write the following problem in tableau form. Which variables would be in the initial basic solution? Min Z = 3x1 + 8x2 s.t. x1 + x2 ≤\le≤ 200 x1 ≤\le≤ 80 x2 ≤\le≤ 60

Artificial variables are added for the purpose of obtaining an initial basic feasible solution.

The variable to enter into the basis is the variable with the largest positive cj - zj value.

When there is a tie between two or more variables for removal from the simplex tableau,

When a set of simultaneous equations has more variables than constraints,

What is an artificial variable? Why is it necessary?

The variable to remove from the current basis is the variable with the smallest positive cj - zj value.

Comment on the solution shown in this simplex tableau. Basis 3 5 9 0 0 9 1/3 2/3 1 1/3 0 40 0 5/3 19/3 0 -1/3 1 100 3 6 9 3 0 360 - 0 -1 0 -3 0

Every extreme point of the graph of a two variable linear programming problem is a basic feasible solution.

Coefficients in a nonbasic column in a simplex tableau indicate the amount of decrease in the current basic variables when the value of the nonbasic variable is increased from 0 to 1.

The basic solution to a problem with three equations and four variables would assign a value of 0 to

A solution is optimal when all values in the cj -zj row of the simplex tableau are either zero or positive.

Comment on the solution shown in this simplex tableau. Basis 4 6 5 0 0 0 3 0 -1 1 -1 26 6 1 1 1 0 -1 10 6 6 6 0 -6 60 - -2 0 -1 0 6

To determine a basic solution set of n-m, the variables equal to zero and solve the m linear constraint equations for the remaining m variables.

In the simplex method, a tableau is optimal only if all the cj -zj values are

When a system of simultaneous equations has more variables than equations, there is a unique solution.

What coefficient is assigned to an artificial variable in the objective function?

Write the following problem in tableau form. Which variables would be in the initial basis? Max x1 + 2x2 s.t. 3x1 + 4x2 ≤\le≤ 100 2x1 + 3.5x2 ≥\ge≥ 60 2x1 -1x2 = 4 x1 , x2 ≥\ge≥ 0

A basic solution and a basic feasible solution

The purpose of the tableau form is to provide

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance and Operations Management

Advanced Linear Programming Applications

Distribution and Network Problems

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

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Decision Analysis

Multicriteria Decisions

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Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

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Write the following problem in tableau form. Which variables would be in the initial basic solution? Min Z = 3x₁ + 8x₂ s.t. x₁ + x₂ $\le$ 200 x₁ $\le$ 80 x₂ $\le$ 60

The variable to enter into the basis is the variable with the largest positive c_j - z_j value.

The variable to remove from the current basis is the variable with the smallest positive c_j - z_j value.

A solution is optimal when all values in the c_j -z_j row of the simplex tableau are either zero or positive.

In the simplex method, a tableau is optimal only if all the c_j -z_j values are

Write the following problem in tableau form. Which variables would be in the initial basis? Max x₁ + 2x₂ s.t. 3x₁ + 4x₂ $\le$ 100 2x₁ + 3.5x₂ $\ge$ 60 2x₁ -1x₂ = 4 x₁ , x₂ $\ge$ 0