In this post, I will just post a sample code to set a profile option value from the backend.
This is the sample screen shot of the Profile Option Definition.
Navigation :- Application Developer --> Profile --> System
--To set the Profile value at user Level
BEGIN
IF fnd_profile.save (profile_name => 'DIAGNOSTICS',
profile_value => 'Y',
level_name => 'USER',
level_value => 4516) -- User ID from fnd_user table
THEN
DBMS_OUTPUT.put_line ('Success');
ELSE
DBMS_OUTPUT.put_line ('Fail');
END IF;
COMMIT;
END;