Terrible Classes

At my uni, the students travel within their major to the same group of classes for basically all 4 years of their degree.  Which means that I teach English, not by level, but by major.  And some majors are freakishly good at English.  For example, Robotics or Animation.  There are so few of these programs in Korea that it is extremely competitive to get into them and it's only the top students.  Or Nursing, because they all want to go to America to work so obviously they are motivated to learn English.  However, there are some majors that are notoriously bad, like Music, Fire Protection, Security Services, and Sports. 

Most semesters, I'll have one or two of the "good majors" mixed in with 4 or 5 of the average ones and one or two terrible ones.  I generally plan my classes near to the lowest common denominator, such that even the students in the terrible classes should be able to do the homework and pass the tests.  The average majors will find my class a bit of work but not too hard and the top majors will find it outrageously easy. 

My homework this semester is almost non-existent.  Only 2 projects worth 10% each, one small introduction poster and one, 2 minute speech.  And yet, the students in the bad majors will not be bothered to do it.  Even after I give them 2 weeks and warn then 1 week before it's due.  I'm kind of beyond frustrated right now.  And am really not sure as to how to proceed.  Do I give "F" to 1/2 the class and invite stress upon myself as the professors in their major and their assistants starting phoning me or the English department to change their grades?  Or, do I  just curve them all up and only fail the truly terrible ones?  If only I lived in an ideal world where everyone would just do their homework and do a wee bit of studying before the test.

What do other people do out there in similar situations?