let's say i'm just starting out (i'm not a full time manager, i'm a working manager) and my take-home is barely covering my living expenses - every bit of profit is going into maintaining the business
Then you're probably not a full-time manager. You probably also don't have three employees.
if i cut my take-home, the business fails
You have three employees. You make money from them working while you play solitaire on your computer. Otherwise, why did you hire them? You're telling me you didn't build in any margin?
how much of a price increase can i expect my customers to bear?
Impossible to say. You'll have to experiment.