It is good to see that we have at least one thing in common with Silicon Valley firms, namely the Banana hoarding paradox. Eugene Eric Kim has come up with some potential solutions, but he is perhaps unaware of the fine line between not buying enough bananas and buying so many that the fruit flies move in.
We have been wrestling with the optimum fruit buying strategy in both Headshift and our previous company, and the issues are far more complex than they first appear. Aside from the basics, a good selection of nuts and dried fruit helps, but solving the banana paradox remains an unfulfilled goal. Given the half-life of the average banana, its convenience (no washing necessary, its protective covering doubles as a holder when open, etc.) and desirability, I think the solution might have to be daily or at least thrice-weekly deliveries.
I think we should invest heavily in building out the infrastructure needed to solve this problem. Webvan 2.0 here we come but using only good Caribbean bananas (we built the first version of this site 10 years ago BTW!), not environmentally-unfriendly 'dollar bananas'!

Pah! to these socio-economic solutions - what you need is a good bit of kit:
http://www.presentsformen.co.uk/brand/4/product-PFM-Banana-Guard-4434/