How to deal with students who refuse to do anything except take exams?

Welcome to higher education! Students will use formal assesement to guide their learning, and no amount of cajoling, or appealing to their sense professional or intellectual propriety will change that. Some students will always work above and beyond what the assessment requires of them, but most won't.

Assessment is how students comprehend what is the stated aim of a course. Instead of fighting against it, you might embrace it. For each learning outcome there should be an assessment that is aligned with that outcome - that is, it is impossible to successfully complete the assessment without have met the learning outcome. The learning activities are then designed to meet the outcomes. This might seem like "teaching to the test", but in fact it is the opposite: in "teaching to the test", the assessment defines learning outcomes, here the learning outcomes define the assessment. Biggs and Tang [1] refer to this as "constructive alignment". [1] is a good read for the evidence that students have more or less always measured what they are supposed to learn by what they are assessed on.

Thus you would ask "what learning outcome am I hoping my students achieve by this homework, and where is that assessed?". If the learning outcome isn't assessed anywhere, then it should be. If it doesn't meet a learning outcome then perhaps it shouldn't be set.

In practice we either make homework credit bearing (even if only a tiny percent of the overall credit), or, more frequently, ask an exam question that tests the learning outcome that a homework is aimed towards, and a student won't be able to answer without having done the homework. The final possibility is that the homework is practice for what will be tested in the exam. In this case you need to make this abundantly clear to the students. Even then, you will probably only get a fraction of the class doing it. The consolation is that this is the part of the class that deserves to do better in the exam and undoubtedly will.

[1] Biggs, J and Tang, C. (2011): Teaching for Quality Learning at University, (McGraw-Hill and Open University Press, Maidenhead)

I think your perspective on this is a bit skewed. Other answers have touched on why your assessment probably needs tweaking, but I'd like to address your general view on your students and what you see as their obligations to you.

First, it's important to be clear about your grading rubric at the very beginning of the course. It's okay to announce extra credit work in the middle of the course, but you still need to make that clear when you give out the assignment, not afterwards. You like comparing your course to the workplace, so imagine this: at the beginning of the year, you sit down with your supervisor and decide metrics for how you'll be judged at your review at the end of the year. You both agree on what tasks are important and will be used to rate your performance: task X will count for 50% of your rating, task Y will count for 30%, and Z will count for 20%. Now imagine a month later, your supervisor chews you out for not doing something that was never even mentioned in your agreement, and he tells you that it will be considered in your rating after all. That'd be completely unfair, right? Even if it was something he asked you to do, if he stated it was simply to increase your understanding of something and you wouldn't be paid to do it, then most people would consider that to be voluntary. If it's mandatory and will affect their grade, be clear about that at the beginning. Probably nobody would've objected if you'd done that.

Secondly, students don't have infinite amounts of time and energy to spend on your course. They may have multiple courses, families, jobs, spouses, hobbies, volunteer work, or any other number of reasons to not spend all their resources on your course. Moreover, it isn't a job, you aren't their boss, they aren't being paid to be there, and they aren't delivering anything that you need. So it is completely up to each individual student whether any particular task provides enough benefit (either in increased understanding or as points towards a certification) to be worth the resources it takes to complete it. This isn't unprofessional or a personal insult against you. It's simply rational prioritizing. If this causes them to have poor understanding or to fail the course, that's on them. They're adults, they can make their own decisions and accept the consequences. You don't need to chew them out for not doing extra work; that's unprofessional and inappropriate on your part. In fact, they can simply stop participating at all halfway through if they decide that's the best thing for them, and that wouldn't be unprofessional like not coming into work with no explanation would be. Grade them appropriately and move on.

Your obligations to your students are a clear grading rubric and the tools to succeed in your course. Their obligation to you is to not disrupt your class and to accept a fair grade for the work they submitted. (And you should both treat each other with general basic respect, of course, but that applies to all situations.) That's it. They don't owe you effort or completed assignments, and you don't owe them handholding. Give them the best chance at success that you can (within your own time constraints), and let them decide whether to take the steps necessary to achieve that success.

I guess that most of the students are obliged to take your course, right?

They do not come out of interest for the topic but because they need the exam.

I have first taught mathematics and later logistics at universities. While most of the mathematics students were interested in the topics, many of the logistics students were not.

At first, I found this disappointing and then I realised that it is legitimate to do not more than one is obliged to do to pass the course. I can try to make the course interesting but I cannot make somebody like it.

When I remember my high school time, I tried to be good at any subject, but there were some which I really did not like and for which I did the minimum amount of work to get the grade I aimed for.

So if three quarters of your course hand in work written in the hour before submission deadline or even don't hand in anything at all (I guess that most students have not even looked at the topic before the day of submission, so it is not strange that you did not receive any questions), just be happy about the quarter who did.