This is a very simple Linear Programing problem, which CVX and the solver it calls easily solves.

So you object to K_car coming out to be 0? That is a result of the model and input data. if Csingle_car is set to 0.25, then optimal K_car is 240, with optimal objective value 480; and if K_car is then also constrained to be equal to 0, the optimal objective value is 600, which is worse, thereby proving that K_car = 0 is not an optimal solution when Csingle_car is set to 0.25. Indeed, in this problem, K_car = 0 only becomes non-optimal (all other inputs being held constant) when Csingle_car is sufficiently large so as to make K_car = 0 not the best way of satisfying the first constraint, because it then makes non-zero K_car worth the non-zero contribution to the 2nd term of the objective, because of a more than offsetting saving to the first term of the objective, as made possible via the first constraint.