Math Problem Statement
If x, y are positive real numbers and 2x+3y=15, find the maximum value of x^{2}y^{3}.
Solution
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Math Problem Analysis
Mathematical Concepts
Optimization
Lagrange Multipliers
Calculus
Constraint Optimization
Formulas
f(x, y) = x^2 y^3
g(x, y) = 2x + 3y - 15
Lagrange system: ∇f = λ∇g
Theorems
Lagrange Multiplier Theorem
Suitable Grade Level
Undergraduate Level (Calculus I/II)
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