CO isotopes are able to probe the different components in protostellar clouds. These components, core, envelope and outflow have distinct physical conditions, and sometimes more than one component contributes to the observed line profile. In this study, we determine how CO isotope abundances are altered by the physical conditions in the different components. We use a 3D molecular line transport code to simulate the emission of four CO isotopomers, (CO)-C-12 J = 2 --> 1, (CO)-C-13 J = 2 --> 1, (CO)-O-18 J = 2 --> 1 and (CO)-O-17 J = 2 --> 1 from the Class 0/1 object L483, which contains a cold quiescent core, an infalling envelope and a clear outflow. Our models replicate James Clerk Maxwell Telescope (JCMT) line observations with the inclusion of freeze-out, a density profile and infall. Our model profiles of (CO)-C-12 and (CO)-C-13 have a large linewidth due to a high-velocity jet. These profiles replicate the process of more abundant material being susceptible to a jet. (CO)-O-18 and (CO)-O-17 do not display such a large linewidth as they trace denser quiescent material deep in the cloud.