Answered: Take the following linear programming…

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

Simplex Algorithm

Take the following linear programming model to its standard form and form the canonical system. Obtain the optimal solution using the simplex method with artificial variables (penal method or two-phase method). Perform each step of the simplex method with artificial variables in tabular form to obtain an optimal solution. Includes tables from all iterations. The use of software to obtain the solution is not allowed. Interpret the solution and write the conclusions of the problem.

Max:

z = 3x₁

Subject to:

2x₁ + x₂ ≥ 6
3x₁ + 2x₂ = 4
x₁, x₂ ≥ 0

Please be as clear as possible. Be ordered in solving the problem. Explain in detail all the steps. Thank you very much

Expert Solution

Step 1: Introduction

Max:

$z equals 3 x subscript 1$

subject to:

$2 x subscript 1 space plus space x subscript 2 space greater or equal than space 6 space 3 x subscript 1 space plus space 2 x subscript 2 space equals space 4 space x subscript 1 comma space x subscript 2 space greater or equal than space 0$