1- Which algorithm has better performance in a Big-Oh sense?

2- Work out exact conditions when one package actually outperforms the other and recommend the best choice if up to n = 10^9 items should be processed.

Please show step by step.

Software packages A and B of complexity O(nlogn) and O(n), respectively, spend exactly TA(n)=cAnlog10n and TB(n)=cBn milliseconds to process n data items. During a test, the average time of processing n=104 data items with the package A and B is 100 milliseconds and 500 milliseconds, respectively. Work out exact conditions when one package actually outperforms the other and recommend the best choice if up to n=109 items should be processed