Write a simplex matrix for the following standard maximization problem: Maximize f = lx – 2y subject to the constraints %3D 5x + 2y < 26 5х + 6у < 31 x > 0 y > 0 00 00
Write a simplex matrix for the following standard maximization problem: Maximize f = lx – 2y subject to the constraints %3D 5x + 2y < 26 5х + 6у < 31 x > 0 y > 0 00 00
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
Topic Video
Question
![### Simplex Matrix for Standard Maximization Problem
This tutorial will guide you through writing a simplex matrix for the following standard maximization problem:
**Objective:**
Maximize \( f = 1x - 2y \)
**Constraints:**
\[
\begin{aligned}
5x + 2y &\leq 26 \\
5x + 6y &\leq 31 \\
x &\geq 0 \\
y &\geq 0 \\
\end{aligned}
\]
**Step-by-Step Process:**
1. **Restate the Objective Function:**
The objective function \( f = 1x - 2y \) needs to be converted for simplex method calculations. Typically, this is written with the equation \( f - 1x + 2y = 0 \).
2. **Introduce Slack Variables:**
Each inequality constraint can be converted into an equality by adding slack variables. Let \( s_1 \) be the slack variable for the first constraint, and \( s_2 \) for the second constraint:
\[
5x + 2y + s_1 = 26
\]
\[
5x + 6y + s_2 = 31
\]
3. **Formulate the Simplex Matrix:**
The objective function and constraints can now be expressed in matrix form:
| Basic Variables | x | y | \(s_1\) | \(s_2\) | RHS |
|-----------------|:---:|:---:|:---------:|:---------:|:----:|
| \(s_1\) | 5 | 2 | 1 | 0 | 26 |
| \(s_2\) | 5 | 6 | 0 | 1 | 31 |
| \(f\) | -1 | 2 | 0 | 0 | 0 |
**Graph/Diagram Explanation:**
The blank table in the image represents the simplex tableau, which will be filled with the coefficients from the equations derived above. Each row corresponds to one of the constraints or the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f280fe7-33d7-45ee-88a8-46c08afcb827%2F6292c069-6db6-4434-936f-ae05c8352f95%2Fiyz3i74_processed.png&w=3840&q=75)
Transcribed Image Text:### Simplex Matrix for Standard Maximization Problem
This tutorial will guide you through writing a simplex matrix for the following standard maximization problem:
**Objective:**
Maximize \( f = 1x - 2y \)
**Constraints:**
\[
\begin{aligned}
5x + 2y &\leq 26 \\
5x + 6y &\leq 31 \\
x &\geq 0 \\
y &\geq 0 \\
\end{aligned}
\]
**Step-by-Step Process:**
1. **Restate the Objective Function:**
The objective function \( f = 1x - 2y \) needs to be converted for simplex method calculations. Typically, this is written with the equation \( f - 1x + 2y = 0 \).
2. **Introduce Slack Variables:**
Each inequality constraint can be converted into an equality by adding slack variables. Let \( s_1 \) be the slack variable for the first constraint, and \( s_2 \) for the second constraint:
\[
5x + 2y + s_1 = 26
\]
\[
5x + 6y + s_2 = 31
\]
3. **Formulate the Simplex Matrix:**
The objective function and constraints can now be expressed in matrix form:
| Basic Variables | x | y | \(s_1\) | \(s_2\) | RHS |
|-----------------|:---:|:---:|:---------:|:---------:|:----:|
| \(s_1\) | 5 | 2 | 1 | 0 | 26 |
| \(s_2\) | 5 | 6 | 0 | 1 | 31 |
| \(f\) | -1 | 2 | 0 | 0 | 0 |
**Graph/Diagram Explanation:**
The blank table in the image represents the simplex tableau, which will be filled with the coefficients from the equations derived above. Each row corresponds to one of the constraints or the
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
