d. Consider the primal problem below. The application of the simplex method to the primal requires the use of an artificial variable in the second constraint of the standard primal to secure a starting basic solution. Show that the presence of an artificial primal in equation form variable does not affect the definition of the dual because it leads to a redundant dual constraint. Maximize z = 5x₁ + 12x2 + 4x3 Subject to Primal Dual Problem X1 + 2x2 + x3 10 2X1 X2 + 3x3 = 8 X1, X2 ≥ 0 Primal in Equation Form Dual Variables
d. Consider the primal problem below. The application of the simplex method to the primal requires the use of an artificial variable in the second constraint of the standard primal to secure a starting basic solution. Show that the presence of an artificial primal in equation form variable does not affect the definition of the dual because it leads to a redundant dual constraint. Maximize z = 5x₁ + 12x2 + 4x3 Subject to Primal Dual Problem X1 + 2x2 + x3 10 2X1 X2 + 3x3 = 8 X1, X2 ≥ 0 Primal in Equation Form Dual Variables
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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Write the dual for the following primal problem
Transcribed Image Text:d. Consider the primal problem below. The application of the simplex method to the
primal requires the use of an artificial variable in the second constraint of the
standard primal to secure a starting basic solution. Show that the presence of an
artificial primal in equation form variable does not affect the definition of the dual
because it leads to a redundant dual constraint.
Maximize z = 5x₁ + 12x2 + 4x3
Subject to
Primal
Dual Problem
X₁ + 2X2 + X3 ≤ 10
2x₁ - x₂ + 3x3 = 8
X1, X2 ≥ 0
Primal in Equation Form
Dual Variables
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