Use the indicated entry as the pivot and perform the pivoting. X₁ X2 X3 S₁ z $2 1 2 4 1 0 0 66 2 2 1 0 1 0 54 6 -7 -5 0 0 1 0 Complete the following simplex tableau to show the result of the pivoting. x₁ X₂ X3 (Simplify your answers.) min 4 4 =
Use the indicated entry as the pivot and perform the pivoting. X₁ X2 X3 S₁ z $2 1 2 4 1 0 0 66 2 2 1 0 1 0 54 6 -7 -5 0 0 1 0 Complete the following simplex tableau to show the result of the pivoting. x₁ X₂ X3 (Simplify your answers.) min 4 4 =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Simplex Method for Linear Programming
For this educational example, we will demonstrate how to perform a pivot operation in the simplex method. Below is a simplex tableau that requires pivoting to proceed towards finding the optimal solution.
---
#### Initial Simplex Tableau:
\[
\begin{array}{c|cccccc|c}
& x_1 & x_2 & x_3 & s_1 & s_2 & z & \\
\hline
& 1 & 2 & 4 & 1 & 0 & 0 & 66 \\
& \textcolor{cyan}{2} & \textcolor{cyan}{2} & 1 & 0 & 1 & 0 & 54 \\
& -6 & -7 & -5 & 0 & 0 & 1 & 0 \\
\end{array}
\]
The entry in cyan (2) is chosen as the pivot element.
---
#### Completing the Simplex Tableau:
Following the standard simplex algorithm steps, we pivot around the selected element to form the new simplex tableau.
**Step-by-Step Explanation:**
1. **Pivot on the chosen element (2) at row 2, column 1 (x_1):**
- Divide the entire pivot row by the pivot element to make the pivot element equivalent to 1.
2. **Perform row operations to make all other entries in the pivot column (x_1) equal to 0:**
- Update the remaining rows by subtracting appropriate multiples of the new pivot row.
---
#### Resultant Simplex Tableau:
\[
\begin{array}{c|cccccc|c}
& x_1 & x_2 & x_3 & s_1 & s_2 & z & \\
\hline
& 1 & 2 & 4 & 1 & 0 & 0 & 66 \\
& 1 & 1 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & 27 \\
& -6 & -7 & -5 & 0 & 0 & 1 & 0 \\
\end{array}
\]
**Note:**
- The diagram above illustrates the initial simplex tableau and requires you to complete the tableau after performing the pivot operation.
- The tableau displays variables \( x_1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F132027c3-2ed1-42c8-912e-c4831680baff%2Fc3d8c476-1701-416f-8378-4e53b3890ead%2Fb6ja15o_processed.png&w=3840&q=75)
Transcribed Image Text:### Simplex Method for Linear Programming
For this educational example, we will demonstrate how to perform a pivot operation in the simplex method. Below is a simplex tableau that requires pivoting to proceed towards finding the optimal solution.
---
#### Initial Simplex Tableau:
\[
\begin{array}{c|cccccc|c}
& x_1 & x_2 & x_3 & s_1 & s_2 & z & \\
\hline
& 1 & 2 & 4 & 1 & 0 & 0 & 66 \\
& \textcolor{cyan}{2} & \textcolor{cyan}{2} & 1 & 0 & 1 & 0 & 54 \\
& -6 & -7 & -5 & 0 & 0 & 1 & 0 \\
\end{array}
\]
The entry in cyan (2) is chosen as the pivot element.
---
#### Completing the Simplex Tableau:
Following the standard simplex algorithm steps, we pivot around the selected element to form the new simplex tableau.
**Step-by-Step Explanation:**
1. **Pivot on the chosen element (2) at row 2, column 1 (x_1):**
- Divide the entire pivot row by the pivot element to make the pivot element equivalent to 1.
2. **Perform row operations to make all other entries in the pivot column (x_1) equal to 0:**
- Update the remaining rows by subtracting appropriate multiples of the new pivot row.
---
#### Resultant Simplex Tableau:
\[
\begin{array}{c|cccccc|c}
& x_1 & x_2 & x_3 & s_1 & s_2 & z & \\
\hline
& 1 & 2 & 4 & 1 & 0 & 0 & 66 \\
& 1 & 1 & \frac{1}{2} & 0 & \frac{1}{2} & 0 & 27 \\
& -6 & -7 & -5 & 0 & 0 & 1 & 0 \\
\end{array}
\]
**Note:**
- The diagram above illustrates the initial simplex tableau and requires you to complete the tableau after performing the pivot operation.
- The tableau displays variables \( x_1
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