a math problem

It's easy...

All you've got to do is shove a bunch of bananas in his stomach and feed him a 1,000.

Well, I started out doing one thing, which was wrong as it led me to realize that the first thing I probably want to do is see how far Joe Camel can get 2,000 bananas. Here is what I ended up with:

I start out by assuming that to get to Joe's first drop-off point, he is going to have to make three trips. He will get there, go back, get there again, go back, and get there one last time. I want Joe to get there with 2000 bananas, as that is exactly twice what he can carry. Since Joe is going to need to eat 5 bananas times the distance of dropoff point A, and joe gets to eat 1,000 of the bananas, that means point A is at 1,000 / 5 = 200 miles.

Here is how he does it:

Joe picks up 1,000 cigarettes, er...bananas and drops 2 off each mile. Joe travels 200 miles. Joe has used up 600 banananas and, drops 400 on the ground at point. Joe goes back to the start, eating bananas off the ground.

Joe picks up another 1,000 bananas, and eats 200 of them on the way to point A. Joe drops another 800 bananas at point, which leaves a pile of 1200 bananas.

Joe goes back, eating the last remaining bananas that he left on the ground on the first trip.

Joe picks up the last 1,000 bananas, and when he gets to point A, 800 of those remain. Added to the 1200 there, 2000 bananas remain. 800 miles of desert remain.

Joe takes 1000 bananas and drops 1 on the ground every mile. At point B, 333 miles from point A, he drops 2, leaving 333 to carry back, which he eats on the way.

Joe picks up the last 1,000 and eats bananas off the ground back to point B, 533 miles from the starting point. There are 1,001 bananas at point B now, so one will go to waste. Too bad, Joe!

Joe travels the last 467 miles with a full load, arriving at his destination with 533 bananas.

Here's the details:

Start the camel out with 1000 bananas.

Walk to point A (200 miles) consuming 200 bananas.
You'll have 800 at this point. Drop 600 bananas here.
Now return 200 miles to the start eating your remaining bananas.
(A has 600 bananas)

Now retrieve another 1000 bananas from the start

Walk to the 200 mile mark consuming 200 bananas.
You'll have 800 at this point. Pick up 200 bananas to replenish back to 1000
(A has 400 bananas)

Continue on another 333 1/3 miles to point B (533 1/3 mile mark). Drop 333 1/3 bananas here and return to the 200 mile mark.
(B has 333 1/3 bananas)

Pick up 200 bananas to return to the start.
(A has 200 bananas)

Get a new batch of 1000 bananas.

Walk again to the 200 mile mark. You'll be at 800 but you can replenish to 1000.
(A has 0 bananas)

Walk again to the 533 1/3 mile mark. You'll be at 666 2/3, but then you can replenish with 333 1/3 to be back at 1000 bananas.
(B has 0 bananas, camel is at 533 1/3 mile mark with 1000 bananas).

Now walk the remaining 466 2/3 miles consuming 466 2/3 bananas, but leaving 533 1/3 bananas delivered to the other end.

Answer:
A maximum of 533 1/3 bananas can be delivered.gloomy_druid