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1) Find the maximum and minimum of f(x, y) = 16x² + y² subject to the constraint 4x² + y² = 16. Set up and solve using both methods.

1) Find the maximum and minimum of f(x, y) = 16x² + y² subject to the constraint 4x² + y² = 16. Set up and solve using both methods.

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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1) Find the maximum and minimum of \( f(x, y) = 16x^2 + y^2 \) subject to the constraint \( 4x^2 + y^2 = 16 \). Set up and solve using both methods. 2) Find the dimensions of the box with a volume of 500 cm\(^3\) using the least amount of material. Set up and solve using the LaGrange method.
Transcribed Image Text:1) Find the maximum and minimum of \( f(x, y) = 16x^2 + y^2 \) subject to the constraint \( 4x^2 + y^2 = 16 \). Set up and solve using both methods. 2) Find the dimensions of the box with a volume of 500 cm\(^3\) using the least amount of material. Set up and solve using the LaGrange method.
Expert Solution
Step 1

1. Given, 

          f(x, y)=16x2+y2,

  Subject to the constraint, 

          4x2+y2=16.

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