... And so that constraint forces R1 to be zero? Note that finding a solution to the problem originally stated is equivalent to a linear programming problem, which (for such a simple problem) can easily be solved exactly.
Dividing by R₁ + 2R₂ is not linear, and neither is multiplying C by R₁ + 2R₂, nor dividing by that product. But you could maybe formulate a linear objective function that solves this problem correctly, and then you could formulate the component selection problem as a MILP problem and solve it with GMPL/MathProg/GLPK or the COIN-OR tools. Glancing at it, though, it isn't obvious to me how to formulate it linearly. How would you do it?
