$$\begin{array}{ll} \text{maximize} & x^2 + y^2\\ \text{subject to} & 1 \leq 2 x^2 + 4 y^2 \leq 4\end{array}$$
I don't know how to apply the KKT conditions here, maybe there is other method but I´m not sure how to apply it. Thanks for the help you can give me.