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. Consider the problem of maximizing xix, subject to the constraint 2x2 + x3 = 1. Find all critical points for this optimization problem.

. Consider the problem of maximizing xix, subject to the constraint 2x2 + x3 = 1. Find all critical points for this optimization problem.

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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2. Consider the problem of maximizing x²x₂ subject to the constraint 2x² + x3 = 1. Find all critical points for this optimization problem. 3. The preference relation > satisfies monotonicity if for all x, y EX, if xk > yk for all k, then x > y, and if xk > yk for all k, then x > y. The preference relation satisfies strong monotonicity if for all x, y EX, if xkyk for all k and x *y then x >y. Show that preferences represented by min{x1, x2} satisfy monotonicity but not strong monotonicity.
Transcribed Image Text:2. Consider the problem of maximizing x²x₂ subject to the constraint 2x² + x3 = 1. Find all critical points for this optimization problem. 3. The preference relation > satisfies monotonicity if for all x, y EX, if xk > yk for all k, then x > y, and if xk > yk for all k, then x > y. The preference relation satisfies strong monotonicity if for all x, y EX, if xkyk for all k and x *y then x >y. Show that preferences represented by min{x1, x2} satisfy monotonicity but not strong monotonicity.
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