You're building an -story barn with cows. Each cow is assigned to exactly one floor, each floor has at least one cow. Floor requires work, and with cows it takes time. Find the lowest total time. Example: floors with work [, , ], cows.
If you assign , , cows to floors , , , total time = . This problem beautifully illustrates why convexity holds. Adding more cows gives diminishing returns. Think about it: the first cow on a floor cuts time by half, the second cuts it by a third, etc.