Monster Game I

You are playing a game that consists of n levels. Each level has a monster. On levels 1,2,\dots,n-1, you can either kill or escape the monster. However, on level n you must kill the final monster to win the game. Killing a monster takes sf time where s is the monster's strength and f is your skill factor (lower skill factor is better). After killing a monster, you get a new skill factor. What is