Let P be a set of points in the plane, the providers, and let Q be another set of points in the plane, the clients. In general they have different cardinalities. All the providers and clients handle the same good. Each provider p ∈ P has a supply available sp > 0 of the good, each client q ∈ Q has a demand dq > 0 of the good. Assume that the total supply and the total demand is the same. For a given value λ, we want to know whether the providers can satisfy the demand in such a way that each good travels at most a distance λ. This is a maxflow problem and can be phrased as a LP. Find the smallest λ that gives a feasible solution. Generate random instances in the square, disk, etc. and analyze the optimal value. You may also consider the case when suppliers are on one side and clients in another.