hiijacker-
If all bananas can be eaten before the trip starts, let it eat 1,000 and then carry another 1,000 on the trip. The third 1,000 is (I think) a lost cause. That’s because there’s no way to return and get them.
If a banana has to be eaten before each mile it’s trickier.
Let’s break it into steps:
1) Start out with a load of 1,000
2) Proceed 200 miles, at which point there will be 800 left.
3) Set out back to the starting point with 200 bananas for eating on the trip, leaving 600 at the 200 mile point.
4) Repeat steps 1 – 3. You will now be at the starting point with the last 1,000. 1,200 will be at the 200-mile point.
5) Repeat step 1. You will now be at the 200-mile point with 2,000 bananas.
6) I’ll leave the rest for someone else.