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Minimize: C = 6x₁ + 3x2 Subject to the constraints: 4x1 + x₂ > 4 X2 > 2 X1 ≥ 0 x1 X₂ ≥ 0

Minimize: C = 6x₁ + 3x2 Subject to the constraints: 4x1 + x₂ > 4 X2 > 2 X1 ≥ 0 x1 X₂ ≥ 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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Use the simplex method and the Duality Principle to solve the following minimum problem:

**Linear Programming Problem** **Objective:** Minimize the cost function: \[ C = 6x_1 + 3x_2 \] **Constraints:** 1. \( 4x_1 + x_2 \geq 4 \) 2. \( x_2 \geq 2 \) 3. \( x_1 \geq 0 \) 4. \( x_2 \geq 0 \) These constraints define the feasible region for the variables \( x_1 \) and \( x_2 \), ensuring they are within allowable limits or conditions. The goal is to find values of \( x_1 \) and \( x_2 \) that minimize the cost function while satisfying all given constraints.
Transcribed Image Text:**Linear Programming Problem** **Objective:** Minimize the cost function: \[ C = 6x_1 + 3x_2 \] **Constraints:** 1. \( 4x_1 + x_2 \geq 4 \) 2. \( x_2 \geq 2 \) 3. \( x_1 \geq 0 \) 4. \( x_2 \geq 0 \) These constraints define the feasible region for the variables \( x_1 \) and \( x_2 \), ensuring they are within allowable limits or conditions. The goal is to find values of \( x_1 \) and \( x_2 \) that minimize the cost function while satisfying all given constraints.
Expert Solution
Step 1: Introduction of the given problem

Minimize C equals 6 x subscript 1 plus 3 x subscript 2

subjected to constrain

4 x subscript 1 plus x subscript 2 greater or equal than 4 x subscript 2 greater or equal than 2 x subscript 1 greater or equal than 0 x subscript 2 greater or equal than 0

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