Adult PC Game: Mandatory Mentor v1.1.2 by Kana Archive

Mandatory Mentor thrusts you into the high-stakes role of tutoring Reina—a hopeless, spoiled, and bratty student who only has seven days to study for and ace the University of Tokyo entrance exam. To eliminate distractions, you and Reina are forcibly exiled to a deserted tropical island to focus entirely on her studies.
Failure means the island becomes your permanent home—where coconuts and ramen are your only companions. Success? A one-way ticket back to civilization.
Will you mold Reina into a star scholar worthy of Tokyo University? Or will you fail miserably and settle into your new career as a Coconut Collector?