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Camel & Bananas

A camel must travel 1000 miles across a desert to the nearest city.
She has 3000 bananas but can only carry 1000 at a time.
For every mile she walks, she needs to eat a banana.
What is the maximum number of bananas she can transport to the city?

If she starts off with 1000 bananas and carries them 1000 miles, she won't be able to return for the rest of them because she won't have any bananas to fuel her trip back. She won't have any bananas to give to her friends either, because she will have eaten them all during the journey. This suggests that the camel needs to cache piles of bananas at certain points in the desert so she can actually move some of them instead of using them all for fuel.

Suppose the camel does this:

Pick up 1000 bananas, go 200 km, drop 600 bananas, return.
Pick up 1000 bananas, go 200 km, drop 600 bananas, return.
Pick up 1000 bananas, go 200 km, drop 800.
Now you have 2000 bananas at 200 km.

Pick up 1000 bananas, go 333 km, drop 334 bananas, return.
Pick up 1000 bananas, go 333 km, drop 667 bananas.
Now you have 1001 bananas at 533 km.

Eat one banana and pick up 1000 bananas, go 467 km, drop 534 bananas.
She now has transported 534 bananas to the city.