What is the solution to this graph question?

Question

Hi everybody, is there anybody who can answer the following problem? I dont know how to start solving it, thank you very much.![the question is in the picture below][2]

Answer 1

Notice $\frac{x_i}{x_i+x_j}\leq1$. So the minimum is reached by the investor with the least amount of cash, so we just have to make sure that the person with the least amount of cash is connected to the second person with the least amount of cash.

So the best graph is a path, label the people $x_1\leq x_2\dots\leq x_n$ according to cash, and the graph you want is the path where $x_1$ is connected exclusively to $x_2$, $x_2$ to $x_3$ and in general $x_i$ with $x_{i+1}$.