Let x be a nondegenerate BFS to a standard form problem min Tx subject to Ax = b x ≥ 0 and let Z _ {i | x; is a nonbasic variable}. Prove that if x is an optimal solution, then the following LPP has an optimal cost of zero: min CT d subject to Ad = 0 di ≥ 0, i Є Z

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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Let x be a nondegenerate BFS to a standard form problem
min
Tx
subject to Ax = b
x ≥ 0
Transcribed Image Text:Let x be a nondegenerate BFS to a standard form problem min Tx subject to Ax = b x ≥ 0
and let Z
_
{i | x; is a nonbasic variable}. Prove that if x is an optimal
solution, then the following LPP has an optimal cost of zero:
min
CT d
subject to Ad = 0
di ≥ 0, i Є Z
Transcribed Image Text:and let Z _ {i | x; is a nonbasic variable}. Prove that if x is an optimal solution, then the following LPP has an optimal cost of zero: min CT d subject to Ad = 0 di ≥ 0, i Є Z
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