Final answer:
The hotel management is considering the economic feasibility of replacing their checkout system with a new one.
Step-by-step explanation:
The type of feasibility presented in this scenario is Economic feasibility. Economic feasibility focuses on whether the costs of implementing a new system can be recouped in the long run. In this case, the hotel's management is considering whether the investment in a state-of-the-art checkout system will be economically beneficial, considering their loyal customer base and relative monopoly in the region.