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1) @ê Consider the set X = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X₁, X2, X3, X4 = {0, 1}}. Show that x₁ + x2 + x3 ≤ 2 is a valid inequality for X. Show that conv(X) is a full-dimension polyhedron.

1) @ê Consider the set X = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X₁, X2, X3, X4 = {0, 1}}. Show that x₁ + x2 + x3 ≤ 2 is a valid inequality for X. Show that conv(X) is a full-dimension polyhedron.

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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1) Consider the set X = {x E R* / 93.x1 + 34x2 + 26x3 + 18x4 < 131, x1, x2, X3, X4 E {0, 1}}. (a) Show that x1 + x2 + x3 < 2 is a valid inequality for X. (b) Show that conv(X) is a full-dimension polyhedron. (c) Show that the valid inequality x1 + x2 + x3 < 2 is a facet of conv(X).
Transcribed Image Text:1) Consider the set X = {x E R* / 93.x1 + 34x2 + 26x3 + 18x4 < 131, x1, x2, X3, X4 E {0, 1}}. (a) Show that x1 + x2 + x3 < 2 is a valid inequality for X. (b) Show that conv(X) is a full-dimension polyhedron. (c) Show that the valid inequality x1 + x2 + x3 < 2 is a facet of conv(X).
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