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Consider the following linear optimization model: (P) max s.t. x1 + 2x₂ -x1+x₂ ≤ 6 x1 − 2x₂ ≤ 4 - X1, X2 > 0.

Consider the following linear optimization model: (P) max s.t. x1 + 2x₂ -x1+x₂ ≤ 6 x1 − 2x₂ ≤ 4 - 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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show the mechanical steps not the table method please

Consider the following linear optimization model: (P) max s.t. x1 + 2x₂ -x1 + x₂ ≤ 6 x12x₂ < 4 X1, X2 ≥ 0.
Transcribed Image Text:Consider the following linear optimization model: (P) max s.t. x1 + 2x₂ -x1 + x₂ ≤ 6 x12x₂ < 4 X1, X2 ≥ 0.
Use the simplex algorithm (starting from the basis composed of slack variables) to show that (P) is unbounded. When multiple variables are eligible to enter the basis, select the eligible variable with highest reduced cost. If multiple variables are eligible to leave the basis, select the eligible variable whose index is smallest. (When providing an answer to this problem, report (at least) the simplex dictionary obtained at each iteration, and state what variables are entering/leaving the basis.)
Transcribed Image Text:Use the simplex algorithm (starting from the basis composed of slack variables) to show that (P) is unbounded. When multiple variables are eligible to enter the basis, select the eligible variable with highest reduced cost. If multiple variables are eligible to leave the basis, select the eligible variable whose index is smallest. (When providing an answer to this problem, report (at least) the simplex dictionary obtained at each iteration, and state what variables are entering/leaving the basis.)
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