$7.$ Consider a set of mobile computing clients in a certain town who each need to be connected to one of several possible base stations. We$$ll suppose there are n clients, with the position of each client specified by its $($x$,$ y$)$ coordinates in the plane. There are also k base stations; the position of each of these is specified by $($x$,$ y$)$ coordinates as well.

For each client, we wish to connect it to exactly one of the base stations. Our choice of connections is constrained in the following ways.

There is a range parameter r$$ that is a client can only be connected to a base station that is within distance r$.$ There is also a load parameter L$$no more than L clients can be connected to any single base station.

Your goal is to design a polynomial$-$time algorithm in pseudo formatfor the following problem. Given the positions of a set of clients and a set of base stations, as well as the range and load parameters, decide whether every client can be connected simultaneously to a base station, subject to the range and load conditions in the previous paragraph. Please make sure to prove the algorithm and provide the runtime. Some hints: This is an application of max flow problem. Have one vertex for every client and one vertex for every base station. Add two extra vertices s and t$.$ Now, add an edge from s to every client vertex and capacity of this edge is $1.$ Similarly add edges from every base station vertex to t of capacity L$.$ Add an edge from a client vertex to a base station vertex if the client can be assigned to this base station.