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2.x + 2x102 + x- 10x1 – 10x2 s.t. ri+x < 5 max 3x1 + x2 < 6 X1, x2 >0

2.x + 2x102 + x- 10x1 – 10x2 s.t. ri+x < 5 max 3x1 + x2 < 6 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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Consider the following NLP: max 20+ 2x1X2 + x% - 10x1 - 10x2 s.t. a+x < 5 3x1 + x2 < 6 X1, 02 > 0 1 (a) Aside from regularity and the given constraints, what are the first order necessary conditions for this problem? (Be as specific as possible.) (b) Find a solution by assuming the first Lagrangian multiplier constraints is active and the second one is inactive. (c) Does this satisfy the first order necessary conditions? Explain.
Transcribed Image Text:Consider the following NLP: max 20+ 2x1X2 + x% - 10x1 - 10x2 s.t. a+x < 5 3x1 + x2 < 6 X1, 02 > 0 1 (a) Aside from regularity and the given constraints, what are the first order necessary conditions for this problem? (Be as specific as possible.) (b) Find a solution by assuming the first Lagrangian multiplier constraints is active and the second one is inactive. (c) Does this satisfy the first order necessary conditions? Explain.
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