A minimum wage is necessary, but instead of having a single minimum for everyone, it should be adjusted on a sliding scale based on the absolute minimum needs of the individual in question. So lets say a teenager, for example, could be paid less than a single mother trying to raise a couple of kids while working three jobs. This would also enable teenagers to have a chance to build up job experience that they can use later on when they are starting their careers because employers would have an incentive to hire them.
But if they are applying to the same jobs why would the employer take the single mother rather than the teenager.