This is a contentious and highly individual thing, of course, so all answers in this should be taken with a grain of salt. But, if this is your job then:
Why? First, some practical reasons that apply to any job.
- You are not an island. Some topics and/or classes are distasteful to everyone, or at least to everyone who is on the list to teach it. Part of having a real job is sometimes taking on distasteful tasks for good reasons.
- In a well-functioning department, usually one is not asked again and again to do something really personally not preferred, at least not without being excused from something else bad. Roommates all have to pay rent, but maybe one person pays less but then has to take out the garbage.
- Jobs are not just about what you are doing, they are about who you are doing them with. (At least sometimes.) If you have a motivated student to tutor, or one where even while tutoring something boring, you get to see their eyes light up with, "Oh, that's how it works!" then the intrinsic rewards may be substantial. That's a lot different from writing homework problems for LP for a textbook.
- You could get fired, or blacklisted. Let's hope not, but that is a reality. In the wider academic universe, you could be denied tenure (at least, outside the rarified atmosphere of Research I universities).
There is another reason which is important, but which you may not yet be at a point to internalize if you are early in your math teaching/tutoring career.
Sometimes we learn, in teaching something we find boring or distasteful, that there is a rich depth we didn't anticipate. I was not particularly enamored of analysis any of the three times I took it at various levels. But teaching it now, I see how it is really about topology and the very nature of the reals - even if I can't always say that.
You may be wishing you were tutoring someone in real analysis. Fine. But linear programming and optimization in this sense also have huge depth. Go crazy - find real-life data to optimize off of, look into the burgeoning literature on operations research for disaster relief, start learning about integer programming versus "regular" linear programming and polytopes... the world is your oyster. I wish I would have understood this when I taught linear programming in a very similar situation to yours, I think.
Now, this may not convince you, and it may indeed be right that you shouldn't teach this. I shouldn't have taught a stats course in the first five or six years I was teaching, for instance, and I would still not be overly enthusiastic about it. Maybe you have a bad manager. If it is really that distasteful, maybe you need to find a different job (if possible). And of course it wouldn't hurt to be looking elsewhere if you are pretty sure that this will be the most enticing topic you will be tutoring in the near future.
But that sounds like a bit of a stretch from your description. If you are in a well-functioning situation where you otherwise would like to stay and where you will not perpetually be asked to do things you don't like, and perhaps even where there is support for professional development, then just do it. If having to teach something we find boring once in a while sounds bad, then see the 13th panel in this amusing webcomic.