I'd like to write the problem in Latex, outsource it to a freelance coder, and get back the result.
Mathematical programming problems can be written down very precisely and unambigously using mathematical terms, formulas and symbols. That is quite an advantage over the typical business software project, where people often don't know what they want, and use standard english language to describe their requirements in fuzzy ways. The example you linked to shows this well: for a mathematician, those formulas describe the task to be done very clearly.
For outsourcing, this is definitely a good start - assumed you are a trained mathematical writer, you can give a precise, written problem description to someone else. Assumed you are able to describe your specific task in a similar quality as it was done in that example, I am pretty sure that describing your requirements in a precise manner is not the problem you need to solve.
However, to read and understand such a mathematic problem description correctly, one needs a trained expert as well. And in your case, you also want an expert who has experience in programming with mathematica. So you are looking for a highly qualified specialist, with good communication skills - and he should also be cheap. These are quite opposing goals - and that is your main problem.
At places like freelancer.com, you get what you pay for. There are thousands of beginners which lack the necessary expertise, often from low wages countries, trying to make some money and bid for ridiculously low prices, but the experts for your domain are there as rare as elsewhere. So the best recommendation I can give you here is, either
start looking at other places (math students from a nearby university might be an idea?)
invest more time to filter out the low quality responses from freelancers all over the world, and if you are lucky, you find one specialist who can help you after some weeks or months
and expect to pay more than 50$ per project - specialists typically have higher wages/hour, at least at the place where I live. You don't pay them only for the time their invest to solve your task, but also for the years they invested to learn the stuff which is necessary to be able to solve such kind of tasks.
As a final note, don't be astonished when the time and effort you need to invest to find a reliable external freelancer, and the effort you need to invest into the quality assurance of his results, may exceed the time you would have needed to solve those problems by yourself or a a colleague of your at your company.