C++ Algorithm for solving maximisation in linear programming

Question

I am learning about maximisation with linear programming, and have come across an algorithm for maximisation with two variables ( silver and gold in this instance) but I am unsure what a certain section of the code is doing:

using namespace std;


class PreciousStones {
  int n;
  vector<int> as;
  vector<int> ag;

The function below is the section I am unclear on:

  double maxg (double s) {
    double g = 0;
    for (int i=0; i<n; i++)
      if (s == 0)
        g += ag[i];
      else if (as[i] <= s) 
        s -= as[i];
      else {
        g += (1-s/as[i])*ag[i];
        s = 0;
      }
    return g;
  }

The rest of the code is below (for context), if anyone knows of some relevant papers on this algorithm, or can provide a brief explanation on this function I would appreciate it greatly

public:
  double value(vector <int> silver, vector <int> gold) {
    n = silver.size();
    as = silver;
    ag = gold;
    for (int i=0; i<n; i++) 
      for (int j=i+1; j<n; j++) 
        if (as[j]*ag[i] > as[i]*ag[j]) {
          swap(as[i], as[j]);
          swap(ag[i], ag[j]);
        }
    double lo = 0;
    double hi = 51*100;
    double D = 1e-10;
    while (lo+D < hi && lo*(1+D) < hi) {
      double mid = (lo+hi)/2;
      if (mid <= maxg(mid))
        lo = mid;
      else
        hi = mid;
    }
    return lo;
  }
}; 

Answer 1

The magic words you need to google are "Simplex Algorithm" for linear programming constraint maximisation. This slide deck looks like it might be what you want. http://www.cs.nccu.edu/~melikyan/mat_fm/lec/lec5_4.pdf