The problem our capitalist economy faces is not how to feed everyone, but how to make a profit feeding everyone.
Aptly said and so true. We would have no problem feeding everyone on the planet but the capitalists can’t make a profit that way and this goes for most goods.
Just look at the situation with Intellectual Property where the right holders are trying to reign in infinite goods just because they can’t figure out a business plan to make money out of them.
You're trying the classic Libertarian/Objectivist obfuscation tactic of considering the superstructure of a society to be only as complex as any individual within it it but that is absolutely false. Just because the society is comprised by individuals, it does not mean that it acts like one.
It is the problem of the capitalist system that creates this issue as the necessity for profit is ultimate. We may have the capacity to create abundant food but if this cannot be sold to make a profit, it will not be created at all, hence starvation. Combating world Poverty and famine requires the collaboration of the whole world, Individual action has proven to be inadequate to deal with this issue. In such grand scale issues, it is the whole system that needs to be geared to deal with them and capitalism is nothing but.
The quote exhibits a complete misundestanding of the word 'economy' I'm afraid. An economy, capitalist or not, doesn't face problems itself, it's not a person. Some economies have been designed or shall I say planned, but it is always the people participating in the economy who are the ones that face problems and do or don't achieve their solution. And since acquiring his food at the least cost is a problem that every human faces it follows that a free economy will have the greatest amount of people at liberty to pursue their nutrition in the best way possible. So the "capitalist economy" doesn't preclude people from searching for free or cheap food (they do it all the time) nor does it preclude people from giving food away. It is solely individuall's wishes that make the latter more rare than demanding to be payed for the food you have produced.