I don't think the problem can be formulated as an LP, but I might be wrong.

Does anyone know exactly what topic these problems come under and how to find more like them?

That Div2A can be formulated as an LP, and I solved it by drawing the shape of the feasible region and figuring out the optimum by cases, which (to me at least) I found more "systematic" than the editorial solution. I wish there were more problems that involve concepts from LP but don't require you to code up a generic LP solver (e.g. simplex) to solve them.

I've seen simplex solvers in some ICPC notebooks (Stanford, KTH) but I'm not familiar with the problems that require them.

I also remember this nice problem that is equivalent to counting the number of integer points in an LP feasible region defined by a small number of constraints :) https://codeforces.net/contest/1355/problem/C

It's the minimum of the sum divided by 3 and the sum of the two smaller elements.

The first constraint is obviously true, we take 3 elements every turn.

The second constraint is to avoid taking only one type of medal in a turn. It's only tempting to do this if we have a lot of a certain medal. If such a medal exists, it's optimal on every turn to take 2 of that medal, and 1 of any other medal. This is to make maximal usage of it. So we're constrained by how many of the other medals we have.

vector<ll> v(3);
for (int i=0; i<3; i++) {
    cin>>v[i];
}

sort(v.begin(), v.end());
ll res = min((v[0]+v[1]+v[2])/3, v[0]+v[1]);
cout<<res<<endl;

Is this problem in Codeforces 478C - Table Decorations