Learn Russian: Мы изучаем рынок с целью найти нашего целевого потребителя. - We are studying the market with the aim of finding our target consumer.

Both express purpose, but с целью (with the aim/purpose of) is much more formal. It is typically used in business, academic, or official contexts. In everyday conversation, you would usually just say чтобы найти (in order to find).

Does с целью always have to be followed directly by an infinitive like найти?

You use the infinitive directly after с целью when the subject of both actions is the same (here, we study and we find). If the subjects were different, you would need to use the expanded structure с той целью, чтобы... followed by a past tense verb.

Why do we use the perfective verb найти (to find) instead of the imperfective искать (to look for)?

The goal of the action is the successful result: actually finding the consumer. If you used искать, the sentence would mean "We are studying the market with the aim of looking for our target consumer," which implies the goal is merely the process of searching rather than achieving the result.

Why do the words нашего целевого потребителя have genitive case endings if they are the direct object of найти?