There's one severely under-appreciated factor that favors the first option: computers are commodities that can be acquired very quickly. Almost instantaneously if you're in the cloud. Skilled lower-level programmers are very definitely not commodities, and growing your pool of them can easily take months or years.
And if the problem is big enough, buying hardware will cause operational problems, so you'll need more people. And most likely you're not gonna wanna spend on people, so you get a bunch of people who won't fix the problem, but buy more hardware.
That's why people love the cloud.
And yet, people still regularly choose to go down a path that leads there. Because business decisions are about satisficing, not optimizing. So "I'm 90% sure I will be able to cope with problems of this type but it might cost as much as $10,000,000" is often favored above, "I am 75% sure I might be able to solve problems of this type for no more than $500,000," when the hypothetical downside of not solving it is, "We might go out of business."
You can go from 10 -> 12, where a better design would get you from that same 10 -> 50
It's too difficult to renegotiate with computers, too easy to renegotiate with people. When you don't actually know what you need to do, you need people. When you think you know what you need to do, but you're wrong, then you really need people. Most of us are in the latter category, most of the time.
Did the results of the calculations drive that decision?