Any hint for this calculus optimization problem? What should I use? We have a wire mesh of 1000 m to fence 2 regions, one circular and one square. Say how should the mesh should be cut to:
a) The sum of the areas of both fenced regions is maximum.
b) The sum of the areas of both fenced regions is minimum.
I don't know if I should use Lagrange Multpliers or if it's only a one variable calculus problem.
Any hint or idea would be very appreciated. Thank you.

Yes, you can use Lagrange multipliers and yes, it can be expressed as a $1$-variable problem. Your pick.
Let $x$ be the radius of the circle and $y$ the side of the square. We have the constraint
$$2\pi x+4y=1000\tag{1}.$$
We want to maximize/minimize
$$\pi x^2+y^2\tag{2}$$
subject to Condition (1). 
Now use Lagrange multipliers. Things should go smoothly. One must not forget to check the endpoints $x=0$ and $y=0$.
Or else we can use (1) to say solve for $y$ in terms of $x$, and substitute for $y$ in (2). We then have a one-variable problem, to be solved in the usual introduction to calculus way, or some other way. We get a quadratic in $x$, with somewhat messy coefficients. 
