Solve using Lagrange multiplier. Also use an auxiliary function such as the given below. 1. Create the auxiliary function F of four variables x, y, z, and Afor whichF(x, y, z, a) = f(x, y, z) + Ag(x, y, z)2. Establish the system of equations obtained by setting the fourfirst partial derivatives of F equal to zero.F(x, y, z, A) = 0F,(x. y. z, A) = 0|F,(x, y, z, A) = 0F.(x, y, z, A) = 0 ExampleFind the dimensions of the rectangular box with an open top withlargest volume if the total surface area is 216 cm².

Given : Total surface area of the rectangular box is 216 cm²

Answered: Example Find the dimensions of the…

Example Find the dimensions of the rectangular box with an open top with largest volume if the total surface area is 216 cm².

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

Chapter5: Factoring Polynomials

Section5.13: Using Factoring To Solve Problems

Problem 27P

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Question

Solve using Lagrange multiplier. Also use an auxiliary function such as the given below.

1. Create the auxiliary function F of four variables x, y, z, and A
for which
F(x, y, z, a) = f(x, y, z) + Ag(x, y, z)
2. Establish the system of equations obtained by setting the four
first partial derivatives of F equal to zero.
F(x, y, z, A) = 0
F,(x. y. z, A) = 0
|F,(x, y, z, A) = 0
F.(x, y, z, A) = 0

Example
Find the dimensions of the rectangular box with an open top with
largest volume if the total surface area is 216 cm².

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