Use Lagrange multipliers to maximize $ f(x, y) = x + 4xy + 6y $Subject to the constraint $ x + 2y = 5 $

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Description: Use Lagrange multipliers to maximize $ f(x, y) = x + 4xy + 6y $Subject to the constraint $ x + 2y = 5 $

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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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Use Lagrange multipliers to maximize $ f(x, y) = x + 4xy + 6y $

Subject to the constraint $ x + 2y = 5 $

Expert Solution

Step 1

Consider the given information.

$f (x, y) = x + 4 x y + 6 y$ and $x + 2 y = 5$

Now, make the auxiliary function.

$F (x, y, λ) = x + 4 x y + 6 y + λ (x + 2 y - 5)$

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