Minimum Wage?

Is the minimum wage (as set by the federal government) unconstitutional? I can't find the worlds "MInimum Wage" in it, and it would therefore be prohibited by the 10th Amendment. Please don't patronize me with the general welfare argument, because it does not benefit the general welfare, it benefits (if that's how you want to see it) the welfare of a minority of the population. Also, should the government tell private businesses how they should be run? Please answer the question directly.