Yea $350 carpet pad & labor on a 10 x 12 room. that is possible if you do your homework
15 by 14 is 210 Sq ft which is 23.33 yards If installation is 5$ a yard Pad is 3$ a yard. Carpet you get a 12 $ a yard carpet (med. Grade) So right at about 500$ is what you'd be looking at