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.