Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Optimization
Lagrange Multipliers
Multivariable Calculus

Formulas

f(x, y, z) = x^2 + 2y^2 + 3z^2
g1(x, y, z) = x + y + z - 1 = 0
g2(x, y, z) = x - y + 2z - 2 = 0
Lagrange Function: š“›(x, y, z, Ī», Ī¼) = f(x, y, z) + Ī» * g1(x, y, z) + Ī¼ * g2(x, y, z)

Theorems

Method of Lagrange Multipliers

Suitable Grade Level

Undergraduate Level (Calculus III or Multivariable Calculus)