Find the pivot in the simplex tableau. The pivot is. راا X₁ X₂ X3 S₁ S₂ 1 1 1 3 2 0 0 01 4 8 5 4 -3-1 z 022 021 1 18
Find the pivot in the simplex tableau. The pivot is. راا X₁ X₂ X3 S₁ S₂ 1 1 1 3 2 0 0 01 4 8 5 4 -3-1 z 022 021 1 18
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![### Simplex Tableau Pivot Finding
In this exercise, you are required to find the pivot element in a given simplex tableau. The tableau is presented in the following matrix format:
Here is the simplex tableau matrix:
\[
\begin{array}{c|cccccc|c}
& x_1 & x_2 & x_3 & s_1 & s_2 & s_3 & z \\ \hline
& 4 & 8 & 1 & 1 & 1 & 0 & 22 \\
& 5 & 4 & 3 & 2 & 0 & 0 & 21 \\
& -3 & -1 & 0 & 1 & 0 & 1 & 18 \\
\end{array}
\]
**Explanation:**
- The matrix represents a simplex tableau where:
- \(x_1, x_2, x_3\) are decision variables.
- \(s_1, s_2, s_3\) are slack variables.
- \(z\) is the right-hand side of the constraints including the objective function.
**Finding the Pivot Element:**
- The pivot element in the simplex method is used during each iteration to move towards the optimal solution.
- To identify the pivot, follow these steps:
1. Identify the pivot column: This is usually the column with the most negative value in the objective function row (bottom row excluding the rightmost column).
2. Identify the pivot row: This is determined by the minimum positive ratio of the rightmost column element (b-values) to the corresponding coefficient in the pivot column.
Find the specific row and column where these criteria meet, and that element will be your pivot on which the tableau will be manipulated next.
The pivot is
\(\bbox[border: 3px solid #000, padding: 2px]{\text{_____}}\).
Complete the process to locate the exact pivot element in the matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F132027c3-2ed1-42c8-912e-c4831680baff%2F04efa15e-6dfe-43b4-a049-58a2729e57e0%2Fhmmqwkd_processed.png&w=3840&q=75)
Transcribed Image Text:### Simplex Tableau Pivot Finding
In this exercise, you are required to find the pivot element in a given simplex tableau. The tableau is presented in the following matrix format:
Here is the simplex tableau matrix:
\[
\begin{array}{c|cccccc|c}
& x_1 & x_2 & x_3 & s_1 & s_2 & s_3 & z \\ \hline
& 4 & 8 & 1 & 1 & 1 & 0 & 22 \\
& 5 & 4 & 3 & 2 & 0 & 0 & 21 \\
& -3 & -1 & 0 & 1 & 0 & 1 & 18 \\
\end{array}
\]
**Explanation:**
- The matrix represents a simplex tableau where:
- \(x_1, x_2, x_3\) are decision variables.
- \(s_1, s_2, s_3\) are slack variables.
- \(z\) is the right-hand side of the constraints including the objective function.
**Finding the Pivot Element:**
- The pivot element in the simplex method is used during each iteration to move towards the optimal solution.
- To identify the pivot, follow these steps:
1. Identify the pivot column: This is usually the column with the most negative value in the objective function row (bottom row excluding the rightmost column).
2. Identify the pivot row: This is determined by the minimum positive ratio of the rightmost column element (b-values) to the corresponding coefficient in the pivot column.
Find the specific row and column where these criteria meet, and that element will be your pivot on which the tableau will be manipulated next.
The pivot is
\(\bbox[border: 3px solid #000, padding: 2px]{\text{_____}}\).
Complete the process to locate the exact pivot element in the matrix.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
