CALC HELP PLEASE Find the maximum value of the function f(x,y)=ln(xy^2) subject to 2 x^2+7 y^2=8 for x>0 and
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CALC HELP PLEASE Find the maximum value of the function f(x,y)=ln(xy^2) subject to 2 x^2+7 y^2=8 for x>0 and

[From: ] [author: ] [Date: 12-06-06] [Hit: ]
..1/x = λ 4x ..........
Find the maximum value of the function f(x,y)=ln(xy^2) subject to 2 x^2+7 y^2=8 for x>0 and y>0.

Maximum value:

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∇ f = λ ∇ g ...... by the method of Lagrange Multiplers
1/x = λ 4x ...... ∂/∂x ....... eq. (1)
2/y = λ 14y .... ∂/∂y ....... eq. (2)
⇒ 7y² = 4x² ...... divide eq. (1) by eq. (2)
6x² = 8 .... plug into 2x² + 7y² = 8
x = 2/√3 , y = 4/√21

Answer: x = 2/√3 , y = 4/√21
1
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