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The solution to the problem is (x, y, z) = min f(x, y, z) => 00 z) = x² + y² +z_s.t. - 1 -0.5 0.5 -0.75 3 3 1 4' 4' 2 √ x² + 2xy + 2 + 37² = 15/ x+y+z=1 with Lagrange multipliers equal to ₁ = 1 8 and 22 = 9 What is the approximate change of the value function Af, if we change the first constraint to x² + 2xy +z²+² =3 and the second constraint to x+y+z=0.5? 006 8

The solution to the problem is (x, y, z) = min f(x, y, z) => 00 z) = x² + y² +z_s.t. - 1 -0.5 0.5 -0.75 3 3 1 4' 4' 2 √ x² + 2xy + 2 + 37² = 15/ x+y+z=1 with Lagrange multipliers equal to ₁ = 1 8 and 22 = 9 What is the approximate change of the value function Af, if we change the first constraint to x² + 2xy +z²+² =3 and the second constraint to x+y+z=0.5? 006 8

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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The solution to the problem min f(x, y, z) = x² + y². + Z is (x, y, z)= - 1 -0.5 0.5 -0.75 s.t. 3 3 1 4 x² + 2xy + Z² + √² = 15/2 x+y+z=1 1 --/-) with Lagrange multipliers equal to ₁ = " 2 and 22 = 9 What is the approximate change of the value function Af, if we change the first constraint to x² + 2xy + z² + y² = 3 and the second constraint to x+y+z=0.5?
Transcribed Image Text:The solution to the problem min f(x, y, z) = x² + y². + Z is (x, y, z)= - 1 -0.5 0.5 -0.75 s.t. 3 3 1 4 x² + 2xy + Z² + √² = 15/2 x+y+z=1 1 --/-) with Lagrange multipliers equal to ₁ = " 2 and 22 = 9 What is the approximate change of the value function Af, if we change the first constraint to x² + 2xy + z² + y² = 3 and the second constraint to x+y+z=0.5?
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