Fastest structured way to get max(abc) if a+b+c=30

Question

What is the fastest and structured way to get maximum of abc if a+b+c=n, say n=30? a,b,c are non-negative and can be non-integer.

Answer 1

Use that $$\frac{a+b+c}{3}\geq \sqrt[3]{abc}$$ so $$10\geq \sqrt[3]{abc}$$