Use a max flow algorithm to solve the following problem. Elbonia is grappling with a COVID outbreak. It has N affected cities 1,,N. City i has p(i) many patients who require an intensive care bed.

Hospitals in a city i have b(i) many available intensive care beds in total. Transportation of patients living in a city i to a hospital in a city j where they will be treated is possible only if the city j is within K kilometers (by road) from city i.

You are given the above numbers and a map of Elbonia with road distances and have to design an algorithm which assigns each patient from every city i to a sufficiently close city j which has a hospital where that patient can be treated.

Your algorithm should make sure that no city i has to accommodate more patients than its total intensive care unit capacity b(i). It should also output a message impossible if there is no such assignment. In particular: (a) describe what the vertices of the flow graph are; (b) describe what the edges of the flow graph are; (c) describe how the capacities of all edges are assigned; (d) after applying a max flow algorithm describe how the patients are assigned to cities where they will be treated; (e) describe how it is determined that the problem has no solution meeting the constraints given. Note: p(i) can be larger or smaller or equal to b(i); also a patient from a city c(i) does NOT have to be treated in a hospital in the same city.