A final simplex matrix for a minimization problem is given. Find the solution. ху z S1 S2 S3 -f 11 1 4 0 1 0 3 5 5 12 5 0 0 1 4 1 12 - 6 4 6 1 0 0 - 5 2 5 5 6 0 0 0 6 4 1 -770 5 X = y = Z = f =
A final simplex matrix for a minimization problem is given. Find the solution. ху z S1 S2 S3 -f 11 1 4 0 1 0 3 5 5 12 5 0 0 1 4 1 12 - 6 4 6 1 0 0 - 5 2 5 5 6 0 0 0 6 4 1 -770 5 X = y = Z = f =
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A final simplex matrix for a minimization problem is given. Find the solution.
![The text associated with the image is as follows:
---
**A final simplex matrix for a minimization problem is given. Find the solution.**
The matrix is presented in an augmented form, typically used in linear programming for solving such problems.
Matrix layout:
\[
\begin{array}{cccccc|c}
x & y & z & s_1 & s_2 & s_3 & -f \\
\hline
0 & 1 & 0 & \frac{11}{5} & \frac{1}{5} & -\frac{4}{5} & 3 \\
0 & 0 & 1 & \frac{4}{5} & -\frac{1}{5} & \frac{12}{5} & 12 \\
1 & 0 & 0 & -\frac{6}{5} & \frac{4}{5} & \frac{6}{5} & 2 \\
\hline
0 & 0 & 0 & 6 & \frac{6}{5} & 4 & -770 \\
\end{array}
\]
Below the matrix, variables are listed with blank spaces for values:
- \( x = \)
- \( y = \)
- \( z = \)
- \( f = \)
---
**Explanation:**
This matrix represents the final tableau in the simplex method for linear programming. Each row corresponds to a constraint, while the bottom row is the objective function transformed for minimization.
- The first three columns represent the basic variables \( x \), \( y \), \( z \).
- Columns labeled \( s_1 \), \( s_2 \), and \( s_3 \) are slack variables added to transform inequality constraints into equalities.
- The column labeled \(-f\) contains values related to the objective function.
The task involves interpreting the matrix to determine the optimal values for \( x \), \( y \), \( z \), and the minimized function value \( f \).
---
Use this matrix as a calculation exercise to fill in the correct values for \( x \), \( y \), \( z \), and \( f \) based on the simplex solution provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7878796-4071-4397-9fae-1cbeb3b69837%2F7a962134-7e34-4932-8b1f-23cabbd638ca%2Fn5jwrl8_processed.png&w=3840&q=75)
Transcribed Image Text:The text associated with the image is as follows:
---
**A final simplex matrix for a minimization problem is given. Find the solution.**
The matrix is presented in an augmented form, typically used in linear programming for solving such problems.
Matrix layout:
\[
\begin{array}{cccccc|c}
x & y & z & s_1 & s_2 & s_3 & -f \\
\hline
0 & 1 & 0 & \frac{11}{5} & \frac{1}{5} & -\frac{4}{5} & 3 \\
0 & 0 & 1 & \frac{4}{5} & -\frac{1}{5} & \frac{12}{5} & 12 \\
1 & 0 & 0 & -\frac{6}{5} & \frac{4}{5} & \frac{6}{5} & 2 \\
\hline
0 & 0 & 0 & 6 & \frac{6}{5} & 4 & -770 \\
\end{array}
\]
Below the matrix, variables are listed with blank spaces for values:
- \( x = \)
- \( y = \)
- \( z = \)
- \( f = \)
---
**Explanation:**
This matrix represents the final tableau in the simplex method for linear programming. Each row corresponds to a constraint, while the bottom row is the objective function transformed for minimization.
- The first three columns represent the basic variables \( x \), \( y \), \( z \).
- Columns labeled \( s_1 \), \( s_2 \), and \( s_3 \) are slack variables added to transform inequality constraints into equalities.
- The column labeled \(-f\) contains values related to the objective function.
The task involves interpreting the matrix to determine the optimal values for \( x \), \( y \), \( z \), and the minimized function value \( f \).
---
Use this matrix as a calculation exercise to fill in the correct values for \( x \), \( y \), \( z \), and \( f \) based on the simplex solution provided.
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