Hello :) Please solve the optimization problem with the lagrangian method: Objective Function: 0.03 (pi*r^2) + 0.02(2*pi*r*h) Constraints: 1) pi*h*r^(2) = 321620 2) h <= r/2

Hello :) Please solve the optimization problem with the lagrangian method: Objective Function: 0.03 (pir^2) + 0.02(2pirh) Constraints: 1) pihr^(2) = 321620 2) h <= r/2

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter8: Introduction To Functions

Section8.8: Linear And Quadratic Functions

Problem 15OE

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Question

Hello :)

Please solve the optimization problem with the lagrangian method:

Objective Function: 0.03 (pi*r^2) + 0.02(2*pi*r*h)

Constraints:

1) pi*h*r^(2) = 321620

2) h <= r/2

Please show ALL steps! Also, r and h need to be positive. As a reference: Excel solver gives r = 58.9396656 and h = 29.4698328

Thank you :)

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