The Camel-Banana Problem

A camel can carry one banana at a time on its back. It is on a diet and therefore can only have one banana at a time in its stomach. As soon as it has eaten a banana it walks a mile and then it needs a new banana (in order to be able to continue its itinerary). Let there be a stock of N bananas at the border of the desert. How far can the camel penetrate into the desert, starting at this point? (Of course it can form new stocks with transported bananas.)