Why Would Anyone Want to Rake Leaves?
===
To play more interesting video games, of course! Or at least, to obtain the
money necessary to do so. This is what Kevin is trying to prove this autumn, by
offering his neighbours a helping but expensive hand at raking the autumn
leaves. But, being a kid and having to go to school, he only has 6 hours of free
time a day to spend on this task. Plus, he'd really rather spend this time
playing video games. He doesn't really care about the money, that's just a mean
to get better video games. And better leaf-collecting tools.
Price List
---
$40 Game Cube (+5 enjoyment points per hour)
$100 Nintendo DS (+10 enjoyment points per hour)
$300 Nintendo Wii (+100 enjoyment points per hour)
$20 Rake (4 hours and -10 enjoyment points per neighbour)
$60 Leaf Blower (3 hours and -1 enjoyment points per neighbour)
$160 Lawn Tractor (1 hour and +10 enjoyment points per neighbour)
Each of his hours of free time might be spent either
1) playing video games
2) collecting fallen leaves
3) shopping (+1 enjoyment point if he buys a game, none otherwise)
4) doing nothing (no enjoyment points)
At first, Kevin owns no tools nor video games, and has no money. Without tools,
collecting leaves is very long and very painful: it takes all six hours and
causes him to lose 100 enjoyment points.
Collecting the leaves of a single neighbours earns Kevin 20$ (his neighbours are
both rich and generous). If collecting them takes him more than one hour, those
must be consecutive hours within a single day. He has enough rich generous
neighbours to collect leaves every hour of every day if he so wishes.
When shopping, he can buy more than one object if he has enough money.
When playing video games, he can only play with one console at a time.
What is the maximum amount of enjoyment points which he can obtain in n days?