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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.

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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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Please assist with 3 a and b

1. Determine the convexity or concavity property of f(x₁, x₂) = 3(x₁ - 2x₂)² X₁ ER+ i.e.x₁ > 0, x₂ > 0 2. Find and classify all the stationary points of f (x₁, x₂) = ½ (x³ + 8x²) — 2(x² + x²) + 1 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).
Transcribed Image Text:1. Determine the convexity or concavity property of f(x₁, x₂) = 3(x₁ - 2x₂)² X₁ ER+ i.e.x₁ > 0, x₂ > 0 2. Find and classify all the stationary points of f (x₁, x₂) = ½ (x³ + 8x²) — 2(x² + x²) + 1 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).
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