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So how does generating a graph actually solve the problem in the real world? Or am I misunderstanding what the problem is? I was assuming the problem was with some real world application, most likely regarding the implementation of some complex networking algorithm for Heroku's system. But if it's just some abstract math problem, of course it would make sense to use something like Mathematica, MATLAB, etc.

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That was just to demonstrate the problem. You could solve it by using NSolve[expr, vars] and giving a limit for the response time you'd like. You'd get back the number of dyne's you'd need to meet those requirements.

On heroku's side, you could model their network with a few lines of code and experiment with different types of queues to find things that work well and are affordable.

As PG said in beating the averages, it's one o those things that's easy to dismiss when you're looking up the power curve.

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