To elaborate on jejorda2's answer:
I don't think both of these are wrong, but they don't exactly roll off the tongue. I believe, in your example, that
Only a small amount of product is necessary since our formula is highly concentrated with active ingredients.
would be an acceptable use here, although a smoother way to write this sentence could be
Only a small amount of product is necessary since our formula has a high concentration of active ingredients.
But this is an opinion.
I cannot concentrate (in/on) class because of all the noise coming from the hallway.
Here concentrate is being used as a verb, with on being the subject of the concentration and in being the location of the person who is doing the concentrating.
As V0ight has helpfully offered, the use of concentrated in seems to be the preferred method:
Danielle's product is highly concentrated in active ingredients
The majority of low income citizens are concentrated in an area just north of the river.
The cities population boom has been largely concentrated around the area north of the river.
That being said, when using concentrate as a verb, there are plenty of cases where the word with could follow:
I concentrated with a group of my peers to come up with the correct formula.
The formula was concentrated with a large amount of active ingredients.
I will say, at the end of this I have perhaps confused myself more on the subject of concentration