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Minimize: Subject to the constraints: 3x₁ + 2x2 + x3 ≥ 23 X1 + X3 ≥ 10 8x1 + x2 + 2x3 ≥ 40 X1 > 0 C = 4x₁ + x2 + x3 x2 > 0 X3 ≥ 0

Minimize: Subject to the constraints: 3x₁ + 2x2 + x3 ≥ 23 X1 + X3 ≥ 10 8x1 + x2 + 2x3 ≥ 40 X1 > 0 C = 4x₁ + x2 + x3 x2 > 0 X3 ≥ 0

Advanced Engineering Mathematics
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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Question

Consider the following minimum problem (see image below)

Write the dual problem for the above minimum problem by selecting the appropriate number for each blank box shown below (Do not solve the dual problem).

**Objective:** Minimize: \( C = 4x_1 + x_2 + x_3 \) **Subject to the constraints:** \[ \begin{align*} 3x_1 + 2x_2 + x_3 & \geq 23 \\ x_1 + x_3 & \geq 10 \\ 8x_1 + x_2 + 2x_3 & \geq 40 \\ x_1 & \geq 0 \\ x_2 & \geq 0 \\ x_3 & \geq 0 \\ \end{align*} \] This linear programming problem aims to minimize the objective function \( C \) while satisfying all the specified constraints, which are inequalities representing system limitations and non-negativity requirements for \( x_1 \), \( x_2 \), and \( x_3 \).
Transcribed Image Text:**Objective:** Minimize: \( C = 4x_1 + x_2 + x_3 \) **Subject to the constraints:** \[ \begin{align*} 3x_1 + 2x_2 + x_3 & \geq 23 \\ x_1 + x_3 & \geq 10 \\ 8x_1 + x_2 + 2x_3 & \geq 40 \\ x_1 & \geq 0 \\ x_2 & \geq 0 \\ x_3 & \geq 0 \\ \end{align*} \] This linear programming problem aims to minimize the objective function \( C \) while satisfying all the specified constraints, which are inequalities representing system limitations and non-negativity requirements for \( x_1 \), \( x_2 \), and \( x_3 \).
Expert Solution
Step 1: Introduction of the given problem

Minimize C equals 4 x subscript 1 plus x subscript 2 plus x subscript 3

subjected to constrain

3 x subscript 1 plus 2 x subscript 2 plus x subscript 3 greater or equal than 23 x subscript 1 plus x subscript 3 greater or equal than 10 8 x subscript 1 plus x subscript 2 plus 2 x subscript 3 greater or equal than 40 x subscript 1 greater or equal than 0 x subscript 2 greater or equal than 0 x subscript 3 greater or equal than 0

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