Don't you think a week is a very short time to conclude that twitter is 'a total irrelevance for business' - regardless of how many work hours spent?
Twitter may not always return tangible business gains, but it can be a very useful tool for branding purposes, awareness generation, etc.
In my experience, sometimes the silliest tweets get RT'd a lot by kids and adults alike. The only question I ask then, did I word my tweet well enough to get any 'gain' out of it (branding, link, lead-in question, hook, etc?) So, to me, it's not how much or often you tweet, at times it's also how well you tweet.