How Do You Apply Lagrange Multipliers to Optimize a Function with Constraints?

[peace89]

Let f(x,y)= -2x^2-2xy+y^2+2 Use Lagrange multipliers to find the minimum of f subject to the constraint 4x-y = 6

∂F / ∂x =.....
i got -4x-2y+2y but i coming out as wrong what am i missing
∂F/ ∂Y= ...

The function f achieves its minimum, subject to the given constraint, where
x =
y =
λ=
f =
thank you

 

[LCKurtz]

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[peace89]

thanks just sign up here so don't know how things work here. learning

 

[Pyrrhus]

Let f(x,y)= -2x^2-2xy+y^2+2 Use Lagrange multipliers to find the minimum of f subject to the constraint 4x-y = 6

∂F / ∂x =.....

∂F/ ∂Y= ...

The function f achieves its minimum, subject to the given constraint, where
x =
y =
λ=
f =
thank you

Set up your Lagrangean with the equality constraints.

This is a nonlinear program with equality constraints and thus it should be straightforward.

Apply your first order conditions.

Notice you don't need to check the second order conditions (Why?)