a) Identify the basic variables. b) What is the value of x1? c) What is the value of x2? d) What is the value of x3? e) What is the value of P , the optimal solution?
a) Identify the basic variables. b) What is the value of x1? c) What is the value of x2? d) What is the value of x3? e) What is the value of P , the optimal solution?
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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![**Page 1 of 4**
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**2. The Simplex method has produced the matrix below and an optimal solution has been found. Examine the matrix and then answer questions a–e.**
\[
\begin{array}{cccccc|c}
x_1 & x_2 & x_3 & s_1 & s_2 & P \\
\hline
0 & 2 & 1 & 1 & 4 & 0 & 8 \\
1 & 3 & 0 & -0.4 & -2 & 0 & 9 \\
0 & 5 & 0 & 2 & 2.5 & 1 & 44 \\
\end{array}
\]
**a) Identify the basic variables.**
**b) What is the value of \(x_1\)?**
**c) What is the value of \(x_2\)?**
**d) What is the value of \(x_3\)?**
**e) What is the value of \(P\), the optimal solution?**
---
**Explanation of the Matrix:**
The matrix is a tableau used in the Simplex method for linear programming. Each row represents a constraint. The columns are labeled with variables \(x_1\), \(x_2\), \(x_3\), slack variables \(s_1\), \(s_2\), and the objective function value \(P\).
- **Basic Variables:** These are the variables corresponding to the columns with exactly one non-zero entry in each row.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadd942ee-f79e-4a36-9f00-66fe52871351%2F08ff5446-80fa-4cbe-a579-b8c92ab5c570%2Fejr7fy.jpeg&w=3840&q=75)
Transcribed Image Text:**Page 1 of 4**
---
**2. The Simplex method has produced the matrix below and an optimal solution has been found. Examine the matrix and then answer questions a–e.**
\[
\begin{array}{cccccc|c}
x_1 & x_2 & x_3 & s_1 & s_2 & P \\
\hline
0 & 2 & 1 & 1 & 4 & 0 & 8 \\
1 & 3 & 0 & -0.4 & -2 & 0 & 9 \\
0 & 5 & 0 & 2 & 2.5 & 1 & 44 \\
\end{array}
\]
**a) Identify the basic variables.**
**b) What is the value of \(x_1\)?**
**c) What is the value of \(x_2\)?**
**d) What is the value of \(x_3\)?**
**e) What is the value of \(P\), the optimal solution?**
---
**Explanation of the Matrix:**
The matrix is a tableau used in the Simplex method for linear programming. Each row represents a constraint. The columns are labeled with variables \(x_1\), \(x_2\), \(x_3\), slack variables \(s_1\), \(s_2\), and the objective function value \(P\).
- **Basic Variables:** These are the variables corresponding to the columns with exactly one non-zero entry in each row.
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