Explanation Given: The given function is f ( x , y ) = x 2 + 4 x y . The constraint is g ( x , y ) = x + y − 100 . Formula used: The Lagrange function is L ( x , y ) = f ( x , y ) − λ g ( x , y ) Calculation: Consider the Lagrange function for the given function with multiplier λ . L ( x , y ) = x 2 + 4 x y − λ ( x + y − 100 ) L ( x , y ) = x 2 + 4 x y − λ x − λ y + 100 λ The first order partial derivatives of L are L x = 2 x + 4 y − λ L y = 4 x − λ The system of equations is, L x = 0 ; L y = 0 ; g ( x , y ) = 0 L x = 0 ⇒ 2 x + 4 y − λ = 0 ⇒ 2 x + 4 y = λ L y = 0 ⇒ 4 x − λ = 0 ⇒ 4 x = λ ⇒ x = λ / 4 g ( x , y ) = 0 ⇒ x + y − 100 = 0 Substitute the value of x in the equation 2 x + 4 y = λ . 2 x + 4 y = λ ⇒ 2 ( λ / 4 ) + 4 y = λ ⇒ λ 2 + 4 y = λ ⇒ 4 y = λ − λ 2 ⇒ 4 y = λ 2 ⇒ y = λ 8 Substitute the values of x and y in the equation x + y − 100 = 0

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ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 8.6, Problem 2P

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The maximum or minimum value of the function f(x,y)=x2+4xy.

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Chapter 8.6, Problem 1P

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The maximum or minimum value of the function f ( x , y ) = x 2 + 4 x y .

Solution Summary: The author calculates the Lagrange function for the given function with multiplier lambda.

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To find:

The maximum or minimum value of the function f(x,y)=x2+4xy.

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Chapter 8 Solutions

The maximum or minimum value of the function f ( x , y ) = x 2 + 4 x y .

Solution Summary: The author calculates the Lagrange function for the given function with multiplier lambda.

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To find: The maximum or minimum value of the function f(x,y)=x2+4xy.

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Chapter 8 Solutions

To find:

The maximum or minimum value of the function f(x,y)=x2+4xy.