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The crafty math kitties, Eva and Archer, want to cut a rectangular beam with maximal rectangular cross section from an elliptical shaped log with semi-axes of lengths 1 foot and 2 feet. Help the kitties use find the maximal cross-sectional area of such a beam using Lagrange multipliers. Include correct units in your answer and show your work. (Hint: You need to create the cross section function that you want to maximize. And if coordinate axes are set up so the center of the log is at the origin, the log is then bounded by the ellipse 2² +4y² = 4. See the figure below.

The crafty math kitties, Eva and Archer, want to cut a rectangular beam with maximal rectangular cross section from an elliptical shaped log with semi-axes of lengths 1 foot and 2 feet. Help the kitties use find the maximal cross-sectional area of such a beam using Lagrange multipliers. Include correct units in your answer and show your work. (Hint: You need to create the cross section function that you want to maximize. And if coordinate axes are set up so the center of the log is at the origin, the log is then bounded by the ellipse 2² +4y² = 4. See the figure below.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The crafty math kitties, Eva and Archer, want to cut a rectangular beam with maximal rectangular cross section from an elliptical shaped log with semi-axes of lengths 1 foot and 2 feet. Help the kitties use find the maximal cross-sectional area of such a beam using Lagrange multipliers. Include correct units in your answer and show your work. (Hint: You need to create the cross section function that you want to maximize. And if coordinate axes are set up so the center of the log is at the origin, the log is then bounded by the ellipse x² + 4y² = 4. See the figure below.
Transcribed Image Text:The crafty math kitties, Eva and Archer, want to cut a rectangular beam with maximal rectangular cross section from an elliptical shaped log with semi-axes of lengths 1 foot and 2 feet. Help the kitties use find the maximal cross-sectional area of such a beam using Lagrange multipliers. Include correct units in your answer and show your work. (Hint: You need to create the cross section function that you want to maximize. And if coordinate axes are set up so the center of the log is at the origin, the log is then bounded by the ellipse x² + 4y² = 4. See the figure below.
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