# E this problem is solved using the method of lagrange

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Chapter 7 / Exercise 32
Applied Calculus
Berresford/Rockett
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e. This problem is solved using the method of Lagrange multipliers. The Lagrangian is: Φ = 8K + 2L + λ(K.5L.5 - 144) Differentiating with respect to K, L and λ yields: Φ/∂K = 8 + λ(.5L.5/K.5) Φ/∂L = 2 + λ(.5K.5/L.5) Φ/∂ λ = K.5L.5 - 144 Setting these derivatives equal to zero and solving for K, L and λ yields K = 72, L = 288, and TC = 1,152. f. If K = 16, then Q = 4L.5. Thus, for Q = 144, L = 1,296 and TC = 2,720. Diff: 3 Section: 7.6 326 Cha
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Chapter 7 / Exercise 32
Applied Calculus
Berresford/Rockett
Expert Verified