Who cares about real numbers in this context?

If all the numbers that appear in your constraints are rational (p/q with finite p and q), then any solution is also a rational number (with finite nominator and finite denominator).

(Well, any finite solution. Your solution could also be unbounded, then you might have infinities in there.)

A computer can represent finite rational numbers just fine. See eg https://docs.python.org/3/library/fractions.html or https://hackage.haskell.org/package/base-4.20.0.1/docs/Data-... for some libraries.

Though in most cases, people just use floating point numbers in practice, but that's of no philosophical concern.