Integer Problem Solving with two boolean selection variables
Sure, try integer linear programming.  Let $x_{RA1}$ be a zero-or-one variable that is 1 if you select RA1, or 0 if you don't.  Then each of your constraints can be expressed as linear inequalities with these variables.  You can then try applying an off-the-shelf ILP solver.

There are a bunch of other questions on this site with further examples of using ILP to solve combinatorial problems (e.g., Express boolean logic operations in zero-one integer linear programming (ILP)), so feel free to look around.