Dear Members of the community, I am experimenting with Solve[] for the solutions of systems of equalities and inequalities containing parameters. For example

Solve[10 x1 + 3 L1 - L2 - L3 == 0 && L1 (3 x1 - y1 - y2) == 0 && 
  L2 (-x1 + 1/10 y2 + 0.25 y3) == 0 && L3 (0.2 - x1) == 0 && 
  3 x1 - y1 - y2 <= 0 && -x1 + 0.1 y2 + 0.25 y3 <= 0 && 
  0.2 - x1 <= 0 && L1 >= 0 && L2 >= 0 && L3 >= 0, {x1, L1, L2, 
  L3}, Reals]

My variables are { x1,L1,L2,L3} and I am including the parameters {y1,y2,y3}. Mathematica seems to handle this rather complicated solution but also displays the following message:

Solve::ratnz: Solve was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result.

Could someone help me to interpret this?

Is there information concerning the number of parameters I could include in the set of equations? In this case, the functionality given by Solve[] seems very powerful, but not many examples can be found that consider parametric solutions. I will appreciate any help. Cheers

Jesus