Rectangle Maximization

This is an example of the solution of constrained optimization using Alglib.js

A rectangle is to be inscribed in the ellipse \[\frac{x^2}{4}+y^2=1\] Find the maximum area of the rectangle. Let \(x\) and \(y\) denote the intputs to a maximization function \(f(x,y)\) describing the area of the rectangle where \[f(x,y) = 2x*2y.\] Subject to the equality: \[\frac{x^2}{4}+y^2-1=0\]