I'm not an expert in this, so maybe this isn't technically an issue, but it seems like you've been given a bad way to solve the problem (i.e. their choice of x and y). Machine 1 doesn't care what 2 does, and vice versa. So using x as the number of A's produced doesn't tell you anything about what each machine does. (Again, maybe there's a way to do it that way, but I think my approach is at least easier.)

However, number of A's produced on 1 exactly determined number of B's produced on 1. (NB! #B1 is not necessarily just (60-eA)/2, you have to round down!) Same with machine 2. So I would use x=#A1 and y=#A2. Profit is easily determined from those independent variables, and you have the simple 0<=x<=20 and 0<=y<=11 (I think; I'm on mobile).