This is a practice question from my Multivariable Calculus Course. It wants me to use maximization to figure it out, starting with xy + 2xz + 2yz = 192 and using partial derivatives, etc… Thank you. Find the dimensions of an open-topped box that maximizes volume when the surface area is fixed at 192 square centimeters.(width, length, height) = () cm

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Find the dimensions of an open-topped box that maximizes volume when the surface area is fixed at 192 square centimeters ) (width, length, height) = cm

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter63: Volumes Of Pyramids And Cones

Section: Chapter Questions

Problem 25A

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Question

This is a practice question from my Multivariable Calculus Course. It wants me to use maximization to figure it out, starting with xy + 2xz + 2yz = 192 and using partial derivatives, etc… Thank you.

Find the dimensions of an open-topped box that maximizes volume when the surface area is fixed at 192 square centimeters.
(width, length, height) = (
) cm

Study of calculus in one variable to multiple variables. The typical operations involved in multivariate calculus are limits and continuity, partial differentiation, and multiple integration. Major applications are in regression analysis, in finance by quantitative analysis, in engineering and social science to study and build high dimensional systems and exhibit deterministic nature.

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Step 1: Given data

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Step 2: Partial derivative with respect to x

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Step 3: Partial derivative with respect to y

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Step 4: Critical points

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Step 5: Dimension

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