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1. Determine the convexity or concavity property of f(x₁, x₂) = 3(x₁ - 2x₂)² x₁ R₁ i.e.x₂ > 0, x₂ > 0

1. Determine the convexity or concavity property of f(x₁, x₂) = 3(x₁ - 2x₂)² x₁ R₁ i.e.x₂ > 0, 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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Please assist with question 1 and 2 as detailed as possible.

1. Determine the convexity or concavity property of f(x₁, x₂) = 3(x₁ - 2x₂)² X₁ ER+ 2. Find and classify all the stationary points of f (x₁, x₂) = (x³ + 8x³) — 2(x² + x²) + 1 i.e.x₁ > 0, x₂ > 0 3. Consider the function f(x, y, z) = 6xy + 4yz + 6y − 3z² − y² subject to x + 2y + z = 75 a) Write down the first order conditions. b) Determine the nature of the extreme points. 4. Consider the Kuhn-Tucker Probblem Minimum z = (x₁ - 2)² + (x₂ − 1)² Subject to 2x₁ + x₂ ≤ 3 3x₁ + 2x₂ ≥ 5 a) State the Kuhn-Tucker conditions for this problem, b) Verify that (x₁, x₂) = (1, 1) satisfies the conditions in (a). You can now record yourself and your screen at the same time
Transcribed Image Text:1. Determine the convexity or concavity property of f(x₁, x₂) = 3(x₁ - 2x₂)² X₁ ER+ 2. Find and classify all the stationary points of f (x₁, x₂) = (x³ + 8x³) — 2(x² + x²) + 1 i.e.x₁ > 0, x₂ > 0 3. Consider the function f(x, y, z) = 6xy + 4yz + 6y − 3z² − y² subject to x + 2y + z = 75 a) Write down the first order conditions. b) Determine the nature of the extreme points. 4. Consider the Kuhn-Tucker Probblem Minimum z = (x₁ - 2)² + (x₂ − 1)² Subject to 2x₁ + x₂ ≤ 3 3x₁ + 2x₂ ≥ 5 a) State the Kuhn-Tucker conditions for this problem, b) Verify that (x₁, x₂) = (1, 1) satisfies the conditions in (a). You can now record yourself and your screen at the same time
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