Due to the complexity of the problem and the need for optimal resource allocation, the program should implement a variant of the bin-packing algorithm.The simplest implementation of this algorithm is first-fit decreasing (FFD), which sorts the robots in descending order of their capabilities for each task and then allocates the tasks to the first robot that can fulfill their requirements. This method, while fast and easy to implement, does not always produce an optimal solution and may lead to resource wastage.An alternative implementation is the next-fit decreasing (NFD) algorithm, which allocates tasks to the next available robot that can fulfill their requirements. This results in less resource wastage, but may lead to suboptimal use of robot capabilities.A more efficient algorithm is the best-fit decreasing (BFD) algorithm, which sorts the robots in descending order of their capabilities and for each task selects the robot with the smallest amount of free capacity that can fulfill their requirements. This method produces a more optimal solution than FFD and NFD, but also has a higher computational cost.The data structures used will include lists or arrays to store the robots and tasks, as well as priority queues or heaps to implement the sorting required by the algorithm.To optimize the program's resource usage further, dynamic programming could be used to optimize robot movement and task allocation over time.In conclusion, the optimal approach to efficiently allocate and manage resources for Amazon's robotic system would be to implement the best-fit decreasing algorithm, using priority queues or heaps to sort the robots and tasks. Dynamic programming could also be used to optimize the program's resource usage over time. Citations:- Bin-Packing Problem (Wikipedia) - https://en.wikipedia.org/wiki/Bin_packing_problem- Priority Queues (Oracle Java Documentation) - https://docs.oracle.com/en/java/javase/16/docs/api/java.base/java/util/PriorityQueue.html- Dynamic Programming (Wikipedia) - https://en.wikipedia.org/wiki/Dynamic_programming