Minimize C=13x₁ + 2x2 subject to 4x₁ + x₂ ≥25 3x₁ + x₂ 26 x1, x₂ 20 C... a. Form the dual problem. Maximize P= 25 y₁ +6y2 4 y₁ + 3 y₂ ≤13 subject to Y₁+1 y₂ ≤ 2 y1, y2 20 b. Find the solution to the original problem by applying the simplex method to the dual problem. Select the correct choice below and fill in any answer boxes within your choice O Min C = at x₁ = and x₂ = O The optimal solution does not exist.
Minimize C=13x₁ + 2x2 subject to 4x₁ + x₂ ≥25 3x₁ + x₂ 26 x1, x₂ 20 C... a. Form the dual problem. Maximize P= 25 y₁ +6y2 4 y₁ + 3 y₂ ≤13 subject to Y₁+1 y₂ ≤ 2 y1, y2 20 b. Find the solution to the original problem by applying the simplex method to the dual problem. Select the correct choice below and fill in any answer boxes within your choice O Min C = at x₁ = and x₂ = O The optimal solution does not exist.
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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![### Linear Programming Problem: Primal and Dual Forms
#### Primal Problem
**Objective:** Minimize \[ C = 13x_1 + 2x_2 \]
**Subject to:**
\[
\begin{align*}
4x_1 + x_2 & \geq 25 \\
3x_1 + x_2 & \geq 6 \\
x_1, x_2 & \geq 0
\end{align*}
\]
---
#### Dual Problem
**a. Form the dual problem:**
**Objective:** Maximize \[ P = 25y_1 + 6y_2 \]
**Subject to:**
\[
\begin{align*}
4y_1 + 3y_2 & \leq 13 \\
y_1 + y_2 & \leq 2 \\
y_1, y_2 & \geq 0
\end{align*}
\]
---
**b. Solution to the Original Problem Using the Simplex Method applied to the Dual Problem:**
Select the correct choice below and fill in any answer boxes within your choice.
- \(\bigcirc\) Min \( C = \) \[ \_\_\_\_\] \text{at} \( x_1 = \) \[ \_\_\_\_\] \text{and} \( x_2 = \) \[ \_\_\_\_\]
- \(\bigcirc\) The optimal solution does not exist.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49e1171a-c632-491d-85cd-df729265f508%2Ffbd66b71-2a0c-4167-a257-fa3c731634ef%2Fneobhr5_processed.png&w=3840&q=75)
Transcribed Image Text:### Linear Programming Problem: Primal and Dual Forms
#### Primal Problem
**Objective:** Minimize \[ C = 13x_1 + 2x_2 \]
**Subject to:**
\[
\begin{align*}
4x_1 + x_2 & \geq 25 \\
3x_1 + x_2 & \geq 6 \\
x_1, x_2 & \geq 0
\end{align*}
\]
---
#### Dual Problem
**a. Form the dual problem:**
**Objective:** Maximize \[ P = 25y_1 + 6y_2 \]
**Subject to:**
\[
\begin{align*}
4y_1 + 3y_2 & \leq 13 \\
y_1 + y_2 & \leq 2 \\
y_1, y_2 & \geq 0
\end{align*}
\]
---
**b. Solution to the Original Problem Using the Simplex Method applied to the Dual Problem:**
Select the correct choice below and fill in any answer boxes within your choice.
- \(\bigcirc\) Min \( C = \) \[ \_\_\_\_\] \text{at} \( x_1 = \) \[ \_\_\_\_\] \text{and} \( x_2 = \) \[ \_\_\_\_\]
- \(\bigcirc\) The optimal solution does not exist.
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