Math Problem Statement
i have a problem know that w1, w2, w3, h1, h2 >= 0 and w1h1 = 4, w2h1 = 4, w3h2 = 2, w1h2 = 4 minimize (w1+w2+w3)(h1+h2)
can you use lagrange multiplier to solve this ?
Solution
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Math Problem Analysis
Mathematical Concepts
Optimization
Lagrange Multipliers
Algebra
Formulas
Lagrange function: 𝓛(w1, w2, w3, h1, h2, λ1, λ2, λ3, λ4) = (w1 + w2 + w3)(h1 + h2) + λ1(w1h1 - 4) + λ2(w2h1 - 4) + λ3(w3h2 - 2) + λ4(w1h2 - 4)
Partial derivative equations
Theorems
Lagrange Multiplier Theorem
Suitable Grade Level
Advanced Undergraduate / Graduate
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