no solution returned when change the objective but same constraints


I am using docplex in python. I have two different objectives, say total cost and total time, but under same set of constraints. When I input same problem instance, the CPLEX can return a solution when the objective is total cost but no solution found when objective is total time. It looks very strange to me since if the constraints are the same, the feasible solution space should be same. CPLEX returning a solution for total cost means that there is feasible solution existing in this space. So even if i changed the objective, CPLEX should still return a solution right? Could anyone help me on this?

Thank you very much!