The following intermediate tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. (see image) Perform all the necessary pivot and row operations to obtain the final tableau. Then, using the final tableau, answer the following questions: The minimum function value is: The value of x1 in the minimum problem is : The value of x2 in the minimum problem is:
The following intermediate tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. (see image) Perform all the necessary pivot and row operations to obtain the final tableau. Then, using the final tableau, answer the following questions: The minimum function value is: The value of x1 in the minimum problem is : The value of x2 in the minimum problem is:
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
The following intermediate tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. (see image)
Perform all the necessary pivot and row operations to obtain the final tableau. Then, using the final tableau, answer the following questions:
The minimum function value is:
The value of x1 in the minimum problem is :
The value of x2 in the minimum problem is:
![This matrix represents a tableau that might be used in linear programming or optimization problems, typically for the Simplex Method. Here's a breakdown of the tableau:
\[
\begin{array}{c|cccccc}
P & y_1 & y_2 & s_1 & s_2 & RHS \\
\hline
0 & 1 & \frac{2}{5} & \frac{1}{5} & 0 & \frac{2}{5} \\
0 & 0 & \frac{8}{5} & -\frac{1}{5} & 1 & \frac{3}{5} \\
\hline
1 & 0 & -\frac{32}{5} & \frac{9}{5} & 0 & \frac{18}{5} \\
\end{array}
\]
**Explanation:**
- **Columns:**
- \( P \) typically represents the objective function row in Simplex tables.
- \( y_1 \) and \( y_2 \) are decision variables.
- \( s_1 \) and \( s_2 \) are slack variables.
- \( RHS \) stands for Right Hand Side and represents the constants in the constraints.
- **Rows:**
- Each of the first two rows (\( y_1 \) and \( y_2 \)) represent constraints.
- The last row relates to the objective function and indicates the current value of the objective function with respect to the constraints given by the tableau.
This tableau might be used to progress toward finding the optimal solution in a linear programming problem. Each of the numbers in the tableau corresponds to coefficients for the variables in the constraints or objective function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa413bcf-f4d4-4563-8c5c-bfbbe2a7d62c%2Faf1af306-2fbf-492c-9fd8-e052005e8e7d%2Fr32260k_processed.png&w=3840&q=75)
Transcribed Image Text:This matrix represents a tableau that might be used in linear programming or optimization problems, typically for the Simplex Method. Here's a breakdown of the tableau:
\[
\begin{array}{c|cccccc}
P & y_1 & y_2 & s_1 & s_2 & RHS \\
\hline
0 & 1 & \frac{2}{5} & \frac{1}{5} & 0 & \frac{2}{5} \\
0 & 0 & \frac{8}{5} & -\frac{1}{5} & 1 & \frac{3}{5} \\
\hline
1 & 0 & -\frac{32}{5} & \frac{9}{5} & 0 & \frac{18}{5} \\
\end{array}
\]
**Explanation:**
- **Columns:**
- \( P \) typically represents the objective function row in Simplex tables.
- \( y_1 \) and \( y_2 \) are decision variables.
- \( s_1 \) and \( s_2 \) are slack variables.
- \( RHS \) stands for Right Hand Side and represents the constants in the constraints.
- **Rows:**
- Each of the first two rows (\( y_1 \) and \( y_2 \)) represent constraints.
- The last row relates to the objective function and indicates the current value of the objective function with respect to the constraints given by the tableau.
This tableau might be used to progress toward finding the optimal solution in a linear programming problem. Each of the numbers in the tableau corresponds to coefficients for the variables in the constraints or objective function.
Expert Solution
Step 1: Step to find pivot element
Finding the negetive minimum from the last row, let it be
Finding the minimum ratio for this column .
Then we can find the pivot element.
Step by step
Solved in 3 steps
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