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lecture11

# lecture11 - a Method of Lagrange multipliers Suppose we...

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Lecture 10 1 2 : Maximum and Minimum Values Subject to Contraints (Method of Lagrange Multipliers) May 22, 2009 Lecture 10 1 2 : Maximum and Minimum Values Subject to Contr

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Objectives 1 Use the method of Lagrange multipliers to solve optimization problems subject to constraints. Lecture 10 1 2 : Maximum and Minimum Values Subject to Contr
Method of Lagrange multipliers Suppose we wish to find the maximum and minimum values of a function f ( x , y ) along a curve specified by g ( x , y ) = k . Lecture 10 1 2 : Maximum and Minimum Values Subject to Contr

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Method of Lagrange multipliers Suppose we wish to find the maximum and minimum values of a function f ( x , y ) along a curve specified by g ( x , y ) = k . We must find where f is parallel to g . Lecture 10 1 2 : Maximum and Minimum Values Subject to Contr
Method of Lagrange multipliers Suppose we wish to find the maximum and minimum values of a function f ( x , y ) along a curve specified by g ( x , y ) = k . We must find where f is parallel to g . This occurs when f = λ g . Lecture 10 1 2 : Maximum and Minimum Values Subject to Contr

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Unformatted text preview: a Method of Lagrange multipliers Suppose we wish to ﬁnd the maximum and minimum values of a function f ( x , y ) along a curve speciﬁed by g ( x , y ) = k . We must ﬁnd where ∇ f is parallel to ∇ g . This occurs when ∇ f = λ ∇ g . The solution to the optimization problem is the solution to the following set of equations ∇ f = λ ∇ g g ( x , y ) = k Lecture 10 1 2 : Maximum and Minimum Values Subject to Contr a Class exercise Find the maximum and minimum values of the function f ( x , y ) = 4 x + 6 y subject to the constraint x 2 + y 2 = 13. Lecture 10 1 2 : Maximum and Minimum Values Subject to Contr a Class exercise Find the maximum and minimum values of the function f ( x , y ) = 4 x + 6 y subject to the constraint x 2 + y 2 = 13. Answer: f (2 , 3) = 26 is the maximum. f (2 , 3) =-26 is the minimum. Lecture 10 1 2 : Maximum and Minimum Values Subject to Contr a...
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lecture11 - a Method of Lagrange multipliers Suppose we...

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