Question

Lagrange Multiplier question,

Image attached.

Answer 1

Your objective function is:
F(x,y,lambda) = x^2 + y^2 + lambda(xy-1)
Now you can partially differentiate with respect to x, y and lambda and obtain 3 equations, from which you can solve for x, y and lambda.

Answer 2

So how you one integrate with respect to lambda?

Answer 3

You do not integrate. It is a discrete distribution. That's where the summation comes in, from 0 to 5.

Answer 4

sorry, I meant partially differentiate,

Answer 5

Sorry, I was on the wrong wavelength!

Answer 6

the x^2 and y^2 go out (=0) since they do not depend on lambda.
the result is therefore (xy-1), which reduces to the constraint itself (always the case).