For the linear programming problem to the right, (a) Set up the simplex tableau. (b) Determine the particular solution corresponding to the initial tableau. (a) Set up the simplex tableau. X= X u 1 0 COLL#] 0 0 (b) Determine the particular solution corresponding to the initial tableau. x=y=₁z=₁ u=146, v=w= M=0. 9 - 1 y 0 -5 Z 1 1 0 V 0 1 0 0 W 0 0 1 0 M 0 ww. 0 230 0 1 146 Maximize x + 5y-7z subject to the listed constraints. x+y+z≤ 146 7x +z≤ 230 9x + 13y ≤146 x20, y ≥0, z 20 0
For the linear programming problem to the right, (a) Set up the simplex tableau. (b) Determine the particular solution corresponding to the initial tableau. (a) Set up the simplex tableau. X= X u 1 0 COLL#] 0 0 (b) Determine the particular solution corresponding to the initial tableau. x=y=₁z=₁ u=146, v=w= M=0. 9 - 1 y 0 -5 Z 1 1 0 V 0 1 0 0 W 0 0 1 0 M 0 ww. 0 230 0 1 146 Maximize x + 5y-7z subject to the listed constraints. x+y+z≤ 146 7x +z≤ 230 9x + 13y ≤146 x20, y ≥0, z 20 0
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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![The exercise involves solving a linear programming problem using the simplex method. The goal is to maximize the function \( x + 5y - 7z \) subject to the following constraints:
1. \( x + y + z \leq 146 \)
2. \( 7x - z \leq 230 \)
3. \( 9x + 13y \leq 146 \)
4. \( x \geq 0, y \geq 0, z \geq 0 \)
### Steps:
**(a) Set up the simplex tableau:**
The initial simplex tableau is structured as follows:
\[
\begin{array}{cccccccc}
& x & y & z & u & v & w & M \\
\hline
& 1 & 1 & 1 & 1 & 0 & 0 & 0 & | & 230 \\
& 7 & 0 & -1 & 0 & 1 & 0 & 0 & | & 146 \\
& 9 & 13 & 0 & 0 & 0 & 1 & 0 & | & 0 \\
\hline
& -1 & -5 & \text{\tiny\square} & 0 & 0 & 0 & 1 & | & 0 \\
\end{array}
\]
The columns represent the variables \(x\), \(y\), \(z\), and the slack variables \(u\), \(v\), \(w\). The matrix on the right after the bar (\(|\)) indicates the constraints' constants.
**(b) Determine the particular solution corresponding to the initial tableau:**
The solution at the initial tableau is as follows:
\[
x = \text{\tiny\square}, \quad y = \text{\tiny\square}, \quad z = \text{\tiny\square}, \quad u = 146, \quad v = \text{\tiny\square}, \quad w = \text{\tiny\square}, \quad M = 0.
\]
This setup and initial solution form the starting point for applying the simplex method to find the optimal solution to the linear programming problem. The blanks (\(\text{\tiny\square}\)) represent values to be determined through further calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4726056b-a0d8-4167-a534-8f03670a441a%2Ff02e822f-7c73-49d5-95d9-03f874936ea0%2Fdl2dwk_processed.png&w=3840&q=75)
Transcribed Image Text:The exercise involves solving a linear programming problem using the simplex method. The goal is to maximize the function \( x + 5y - 7z \) subject to the following constraints:
1. \( x + y + z \leq 146 \)
2. \( 7x - z \leq 230 \)
3. \( 9x + 13y \leq 146 \)
4. \( x \geq 0, y \geq 0, z \geq 0 \)
### Steps:
**(a) Set up the simplex tableau:**
The initial simplex tableau is structured as follows:
\[
\begin{array}{cccccccc}
& x & y & z & u & v & w & M \\
\hline
& 1 & 1 & 1 & 1 & 0 & 0 & 0 & | & 230 \\
& 7 & 0 & -1 & 0 & 1 & 0 & 0 & | & 146 \\
& 9 & 13 & 0 & 0 & 0 & 1 & 0 & | & 0 \\
\hline
& -1 & -5 & \text{\tiny\square} & 0 & 0 & 0 & 1 & | & 0 \\
\end{array}
\]
The columns represent the variables \(x\), \(y\), \(z\), and the slack variables \(u\), \(v\), \(w\). The matrix on the right after the bar (\(|\)) indicates the constraints' constants.
**(b) Determine the particular solution corresponding to the initial tableau:**
The solution at the initial tableau is as follows:
\[
x = \text{\tiny\square}, \quad y = \text{\tiny\square}, \quad z = \text{\tiny\square}, \quad u = 146, \quad v = \text{\tiny\square}, \quad w = \text{\tiny\square}, \quad M = 0.
\]
This setup and initial solution form the starting point for applying the simplex method to find the optimal solution to the linear programming problem. The blanks (\(\text{\tiny\square}\)) represent values to be determined through further calculations.
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