code: def lowerlim(x, y, z, a, b, c):
      
      if x/a + y/b + z/c > 1:
          B = a + b + c - x - y - z
          C = a*b + a*c + b*c - a*y - a*z - b*x - b*z - c*x - c*y
          D = a*b*c - a*b*z - a*c*y - b*c*x
          r = np.roots([1,B,C,D])
          ll = r[~np.iscomplex(r) & (r>0.)]
          return ll[0].real
      else:
          return 0.
docs: Returns the real positive root of
        x/(a+t) + y/(b+t) + z/(c+t) = 1
      when x/a + y/b + z/c > 1 else zero