The "aware" is fine because it's the beginning of a non-essential clause. The simplest version of the sentence is:
Farmers are switching to newer, more efficient technologies.
So, to simplify it a bit less (still ignoring the type of farmer being discussed) the phrase would be:
Farmers, aware that new developments in agriculture production can result in millions of dollars in additional revenue, are switching to newer, more efficient technologies.
I hope this makes it clearer why no verb is necessary here. Yes, the description of the farmers makes it a bit more complex, but that's part of what they're testing on the SAT. So, now if we add back in the farmer description, it should read more clearly:
Farmers who grow major crops such as corn, rice and wheat, aware that new developments in agriculture production can result in millions of dollars in additional revenue, are switching to newer, more efficient technologies.
So, what if we try to "fix" the non-essential clause?
Let's start by ignoring the actual end of the sentence:
Farmers who grow major crops such as corn, rice and wheat, aware that new developments in agriculture production can result in millions of dollars in additional revenue.
So, in this case, we need to add a verb:
Farmers who grow major crops such as corn, rice and wheat, are aware that new developments in agriculture production can result in millions of dollars in additional revenue.
But now we have to remove a comma, which means we're making two changes to the sentence, rather than one... and we still have this chunk to add to the end:
Farmers who grow major crops such as corn, rice and wheat are aware that new developments in agriculture production can result in millions of dollars in additional revenue, switching to newer, more efficient technologies.
In order for this final part to make sense, we've got to add a lot of words:
Farmers who grow major crops such as corn, rice and wheat are aware that new developments in agriculture production can result in millions of dollars in additional revenue, so they are switching to newer, more efficient technologies.
So, now the sentence makes sense but we've had to make a bunch of changes... which isn't a possible solution to the question. So this can't be the "correct" path.