You could make things clearer by stating which branch of objective function specification you are referring to (options.method value).
Aside from that, your problem is not reproducible, because the input data is not provided. Are you asking for something impossible, such as a constraint that a new car must be bought for less than $1e4, and the problem only becomes feasible when the $1e4 is increased to $2e4?
All but the first section of Debugging infeasible models - YALMIP also applies to CVX.
Also, you should also use the latest version of Mosek 10.x, rather than 9.1.9 which is bundled with CVX. In order to do so, follow the directions in