Can you base a business on government rewards? - for example, NYPD paid 10K to whomever convicts a cop killer.?

FBI is giving away rewards for catching criminals, and many families are offering rewards for finding lost family members; can you start a business that is based on locating (and if appropriate) catching them for the reward? (not like a bounty hunter, this has bigger potential profit); and you help convict criminals, i am assuming that the operations of such business will involve a lot of detective work and perhaps require a private detective license, what do you think?