Final answer:
The logical conclusion is that the library has added the fee to discourage patrons from spending too long on the computers.
Step-by-step explanation:
The logical conclusion that can be derived from the announcement is option c: The library has added the fee to discourage patrons from spending too long on the computers. The announcement states that each person should restrict themselves to 30 minutes on a computer, and there will be a $3 charge for each additional 15-minute period.
This suggests that the library wants to incentivize shorter computer usage to ensure that all visitors have the opportunity to use the limited number of computers. The fee acts as a deterrent to discourage patrons from monopolizing the computers.