I couldn't find a general, fully algebraic solution for the Cobb-Douglas "optimal consumption bundle" problem for n goods online. For sure, this is an easy question which appears in almost every microeconomic theory textbook out there in some form, but seemingly always with more variables determined. In case anyone needs it, I wrote it up. This is an interesting problem in basic multivariable calculus (which is why I wrote it up) because it's an example of a case in which one can maximize a function with an infinite or unknown number of input variables.
Optimal consumption bundles in an n-good Cobb-Douglas model