Maximize profitable pairs

You are given an array profits of n integers representing net profit per item and an integer threshold T. You may form disjoint pairs (i, j). What is the maximum number of pairs such that profits[i] + profits[j] >= T? Describe an O(n log n) algorithm using sorting and a left/right pointer strategy, prove correctness, analyze complexity, and discuss edge cases (odd n, negative values, very large or very small T). Provide pseudocode.