maxr₁ +37₂ ZER² s.t. x² + ax=10
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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how to solve please teach explain step by step

Transcribed Image Text:we solved this for a = 1. We found that z*(a = 1) = (1,3) is a solution with
Lagrange multiplier X* (a = 1) = ¹/2 and a maximum value
f*(a = 1) = f(x*(1)) = f(1, 3) = 10.
We now want to use the envelope theorem to estimate the maximum value at a = 1.01, so to
estimate f*(1.01).
Firs,t note that the NDCQ condition is satisfied whenever a 0 (HW: Verify this!), and
the Lagrangian is given by:
maxr₁ +372
ZER²
s.t. x² + ax = 10
L ((x; a); λ) = f(x; a)-X (g(x; a)- b)
lam1
By the envelope theorem:
Əf*(a)
да
An estimate for f*(1.01) is therefore given by
=
ac
да
84
= x₁ + 3x₂ −X(x² + ax-10)
|z=2*(a),A°=1/2 = −22²2=2(1)-(1.3)
=
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