I saw a post today on the Make blog about a challenge to create an extremely cheap FM/SW radio kit for developing nations. The organization sponsoring the challenge distributes donated wind-up powered Grundig radios, but they're relatively expensive, get stolen, can't be repaired, etc.

The specs they are looking for are certainly challenging, but may all be reasonable except for the power. They are asking that the radio be powered by a single AA battery (it may also have a solar cell) and contain a LED bright enough to use as a small lamp.

You can read the specs here: FM Radio Challenge

My question is whether this community thinks that these specs are just written by non-experts. Is a practical device do-able with that power? Assume the price requirement could be met (the solar cell may be the priciest part). If a single AA was chosen due to its ubiquity, would a high quality rechargeable battery still meet the needs?

And yes, I did really want to put this challenge in front of the readers here by putting it in the form of a real question. Note that it is tagged community wiki.