This letter presents a novel multi-robot task allocation and path planning method that considers robots' maximum range constraints in large-sized workspaces, enabling robots to complete the assigned tasks within their range limits. Firstly, we developed a fast path planner to solve global paths efficiently. Subsequently, we propose an innovative auction-based approach that integrates our path planner into the auction phase for reward computation while considering the robots' range limits. This method accounts for extra obstacle-avoiding travel distances rather than ideal straight-line distances, resolving the coupling between task allocation and path planning. Additionally, to avoid redundant computations during iterations, we implemented a lazy auction strategy to speed up the convergence of the task allocation. Finally, we validated the proposed method's effectiveness and application potential through extensive simulation and real-world experiments. The implementation code for our method will be available at https://github.com/wuuya1/RangeTAP.