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Problem 1. Σvex (f+(v) - ƒ¯(v)) = a) Show that, for any flow f in a network N and any set X CV, f+(X) — ƒ¯(X). (15 points). b) Give an example of a flow f in a network such that Σvex ƒ+(v) ‡ ƒ+(X), and Σvex ƒ¯(v) ‡ ƒ¯(X). (10 points).

Problem 1. Σvex (f+(v) - ƒ¯(v)) = a) Show that, for any flow f in a network N and any set X CV, f+(X) — ƒ¯(X). (15 points). b) Give an example of a flow f in a network such that Σvex ƒ+(v) ‡ ƒ+(X), and Σvex ƒ¯(v) ‡ ƒ¯(X). (10 points).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.3: Systems Of Inequalities
Problem 19E
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Problem 1. Σvex (f+(v) - ƒ¯(v)) = a) Show that, for any flow f in a network N and any set X CV, f+(X) — ƒ¯(X). (15 points). b) Give an example of a flow f in a network such that Σvex ƒ+(v) ‡ ƒ+(X), and Σvex ƒ¯(v) ‡ ƒ¯(X). (10 points).
Transcribed Image Text:Problem 1. Σvex (f+(v) - ƒ¯(v)) = a) Show that, for any flow f in a network N and any set X CV, f+(X) — ƒ¯(X). (15 points). b) Give an example of a flow f in a network such that Σvex ƒ+(v) ‡ ƒ+(X), and Σvex ƒ¯(v) ‡ ƒ¯(X). (10 points).
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