[yabbadu]

We have a glass enclosed lanai and we are thinking about adding some type of carpeting over the cement.

Can anyone recommend type of carpet and company.

Also, if you have this in your home - Are you happy with carpet? Why or Why not?

[villagetinker]

You might want to call the various stores selling carpet and ask what is recommended for this application. Many carpets are not suitable for areas that may get wet, or are damp. If the concrete has not been sealed, it will probably be considered damp. There may be considerations if you have the sliders open all the time (or removed), and if the glass windows are ever opened when rain could get in accidentally.
If you do not want to call the stores, try a Google search for suitable carpet, then you can check for local distributors and installers.