If your doesn't work, do you upgrade your CPU or re-write your code? Sure, if your code sort of works but is maybe only 50% as efficient as you want, go ahead and upgrade your CPU.
But if your code is O(n^3) and just doesn't ever give you an answer, upgrading your CPU is throwing good money after bad.
The current system and people are not able to solve the problem, even after spending >$22k per homeless person per year. How much more do you suggest spending, and why do you think it would make any difference to outcomes?