Lets look at this for a second.... Who are a businesses customers? Hint: It's the people who get paid a wage.
Uhhh, what makes you believe your employees and your customers are the same people? But moving on...
These people get more money, more businesses get more customers. More customers mean more sales. More sales means more profits.
Is it really that hard to grasp that concept?
Yes, because the math doesn't work. At the very best, this would be a break-even. The classic counter-argument is what makes $15 so special? If this works, why not $20? $30? $300? Surely at some point this doesn't keep going and we all get replaced by robots. What makes you think $15 is it? Maybe the optimal point was $5. Maybe it is zero.
Consider this thought experiment. You own a McDonalds. There's probably someone you just hired who's a pretty marginal employee. He or she burns burgers, doesn't wrap them very fast, and is clumsy on the register. You tossed around the idea of hiring the kid or buying that flashy burger flipping machine instead. You figured you'd slot the kid in mid afternoon, there aren't many people coming in so it doesn't matter he or she isn't very efficient, but it was a close call.
Now someone tells you to double that kid's wages. What do you do? That burger flipping machine seems a lot more attractive now. Maybe you'll keep the kid but give him fewer hours. Maybe you'll sadly fire him or her and buy the machine. Once you've bought the machine, you can reduce your staff even in the busy times because the Flip-O-Matic is a sunk cost. That's what economists mean when they say you have to look at things "at the margin". You have to think about what happens to the employee who was just barely worth hiring.
Finally, I think a minimum wage is just wrong on liberty grounds. I've got kids who are just starting out. They've got basically no skills or experience. The only thing they have to offer is their time. $10/hour and something to put on their resumes might be a good deal for them. Who are you and I to tell them the must hold out for $15?