### Simplex Matrix for Standard Maximization ProblemThis 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

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Description: ### Simplex Matrix for Standard Maximization ProblemThis 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

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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

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### 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

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