You increase prices, yes. You might trim the workforce too. But so does every other business that has a large contingent of low skill, low pay labor. This means that most things that are "made on the cheap" become more expensive. So now, the cost of living goes up for everyone who consumes from that pool of resources. This squeezes middle income families and hurts lower income families. Does the cost of living for which a minimum wage worker rise higher than the wage? I don't know. But with a higher cost of living and potentially greater unemployment, I'm not sure that raising minimum wage is a win.
I'm not aware of all the complex reason for why the following is the case, but my brother's mom (I know how odd that may sound) was able to rent an apartment when she was 18 working in fast food without tips. There is _no way in h-e-double-hockey-sticks_ that that could happen anywhere in America today. I'm not convinced that raising minimum wage is the solution -- it could be part of the problem. Models of human behavior and economics can get tricky and counter-intuitive. It is a hard nut to crack; I'll just stick to writing software. Now, if someone wants to pay me to make and become familiar with those models....