At a shipping warehouse, a manager has purchased two warehouse automation robots, an autonomous mobile robot $($AMR$)$ and a pre$-$programmed aerial drone. The AMR can retrieve $21$ packages per hour, and its operating cost is $$3\mathrm{.}50$ per hour. The aerial drone can retrieve $28$ packages per hour, and its operating cost is $$5\mathrm{.}25$ per hour. For each hour of operation, the two robots require technicians to perform maintenance and calibration. The technicians usually spend $5$ minutes to perform maintenance on the AMR after each hour of operation, while the drone requires $12$ minutes of maintenance after each hour. The technicians also work on other warehouse machineries and can only spend $100$ minutes per day to maintain the two robots.

If the warehouse has at least $250$ packages to be retrieved each day, how many hours per day should the manager operate the AMR and drone to minimize the total operating cost? What is the lowest operating cost?