Q/ Calculate the minimum value of the following function f(x, y) = 4(x + y) subject to the equality constraint g(x, y) = x^2 + y^2 -1-0 Using Lagrange multipliers Hint: a typical approach is to consider the constraints into the function using Lagrange multipliers as follows: £= f(x1, x2,.., xn) +A1,2,23..,àn*g(x1, x2... , xn) Where L= Lagrange multiplier. f(xl, x2,..,xn ) = the function to be minimized. g( xl, x2,... xn) = constraints of the function. Then, the values of xl, x2,.., xn and 21A2,23.an are evaluated using partial derivatives as follows: ƏLƏX=0 x=xl, x2,.., xn. 2=11,2,23.,n.
Q/ Calculate the minimum value of the following function f(x, y) = 4(x + y) subject to the equality constraint g(x, y) = x^2 + y^2 -1-0 Using Lagrange multipliers Hint: a typical approach is to consider the constraints into the function using Lagrange multipliers as follows: £= f(x1, x2,.., xn) +A1,2,23..,àn*g(x1, x2... , xn) Where L= Lagrange multiplier. f(xl, x2,..,xn ) = the function to be minimized. g( xl, x2,... xn) = constraints of the function. Then, the values of xl, x2,.., xn and 21A2,23.an are evaluated using partial derivatives as follows: ƏLƏX=0 x=xl, x2,.., xn. 2=11,2,23.,n.
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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Transcribed Image Text:Q/ Calculate the minimum value of the following function
f(x, y) = 4(x + y)
subject to the equality constraint
g(x, y) = x^2 + y^2 - 1 =0
Using Lagrange multipliers
Hint: a typical approach is to consider the constraints into the function using Lagrange multipliers as
follows:
L= f( xl, x2,.., xn) +21,2,23.an*g(x1, x2..., xn)
Where
L= Lagrange multiplier.
f(xl, x2,.., xn) = the function to be minimized.
g( xl, x2,.
Then, the values of xl , x2,.., xn and à 1,12,23.àn are evaluated using partial derivatives as follows:
xn) = constraints of the function.
ƏLƏX=0
X=xl, x2,.., Xn.
2=21,2,23,.an.
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