Answer is 533 and 1/3 banana

If Camel just picks up a load of 1,000 bananas and heads out across the desert, she will eat them all up by the time she gets to the other side. She will also leave 2,000 bananas, unused, to rot back at the oasis. The trick is to use those 2,000 bananas as fuel to get the remaining 1,000 bananas as far across the desert as possible, before Camel makes her final dash for the market.

Camel needs to eat five bananas per mile so long as she is trying to ferry more than 2,000 bananas. Later, when she's hauling between 1,000 and 2,000 bananas, she needs three bananas per mile. And after that, she only eats one banana per mile.

To understand why, let's start at the beginning.

Camel is standing there in the oasis with 3,000 bananas. She picks up the first 1,000. Say she carries them just one mile into the sand, eating one banana. She could drop 999 bananas there, but then she couldn't walk back. So, being a camel with foresight, she drops 998 bananas and keeps one to eat on the return trip.

Now she can pick up the second 1,000 bananas and do the same thing, dropping 998 at the one-mile marker and shambling back to the oasis.

With the third load, there's no return trip: all her bananas have been moved one mile.

How many did she eat up? Five: two on the first round trip, two on the second, and one on the last trip, which is one-way.

She could keep this up, one mile at a time, for 200 miles, by which time she would have used up 1,000 bananas. Or she could just take the first load 200 miles, drop 600 bananas, go back, pick up the next 1,000, etc. Either way, she will find her self at the 200-mile marker with 2,000 bananas.

(Note that there are no monkeys or hungry humans out there in the sand dunes, and no other camels, either. Camel feels her bananas will be safe when she drops a load in the desert and goes back for more.)

Once she has the 2,000 bananas out in the desert, Camel the Mathematical Camel reasons that she now needs three bananas per mile to push her stash farther: 1 round trip for the first load of bananas and 1 one-way trip for the second load. Either with her calculator or with mental math, she determines that she will use up the second 1,000 bananas moving the supply forward 333 1/3 miles. She can either proceed in one-mile increments, or go the whole 333 1/3 miles at once, or anything in between. In the end, Camel finds herself with 1,000 bananas 533 1/3 miles (200 + 333 1/3) into her journey.

It's hot, but Camel takes a deep breath, picks up the 1,000 bananas, and slogs on. This time she can just keep going with no return trips, because she hasn't left any bananas in the desert - just in her stomach.

433 2/3 miles farther on, and lighter by 433 2/3 bananas (she's a nibbler), Camel pads out of the desert and into the market, where a mob of camel-lovers and mathematicians is waiting to pay her handsomely for the 533 1/3 bananas (1,000 - 433 2/3) she has left. She even sells that last 1/3 of a banana to a souvenir hunter from the Annenberg Channel.

In short

533 1/3 bananas well 533 anyway

First leg-out, back, out, back, out. 5 one way trips bananas consumed 1000, bananas moved 2000 1000/5=200 units.
Status 2000 bananas at unit 200

Second leg out, back, out. 3 one way trips
Bananas consumed 1000, bananas moved 1000
1000/3=333 1/3 units
Status 1000 bananas at unit 200+333 1/3=533 1/3

Third les one trip 466 2/3 units (1000-533 1/3)
Bananas consumed 466 2/3
Bananas delivered on far side 533 1/3.  

So you're going to end up leaving bananas in the desert, hoping that there isn't a hungry band of desert monkeys nearby. So you need to travel out with 1000 bananas on your camel and drop some off then come back. so you're gonna need enough left over to get back. The furthest you could go and come back is 500 Km but you wouldn't be able to leave any bananas behind. the idea is that you will pick them up on your next trip, so you want to leave as many out there as you can. It doesn't help if you leave a larger heap of bananas than free space you will have once you get there to pick them up. so you wouldn't want to go 100 Km drop off 800 bananas and come back because you will only be able to pick up 100 of them when you come back by. so the optimal amount of bananas to leave is equal to the distance home from where you leave them. With that said,

Step 1: load up 1000 bananas, go 333 1/3 Km and drop off 333 1/3 bananas and go home.
Step 2: load up another 1000 bananas go 333 1/3 Km and pick up the 333 1/3 bananas you left earlier and go another 111 Km drop off 444 1/3 bananas and go home
Step 3: load up another 1000 bananas go 444 1/3 Km and pick up the 444 1/3 bananas left there earlier and proceed to the market. you will end up selling 444 1/3 bananas and one camel since you won't have any bananas for the trip home.

Hope this helps :)