Consider the problem faced by a hospital that is trying to evaluate whether its blood supply is sufficient. The basic rule for blood donation is the following. A persons own blood supply has certain antigens present; a person cannot receive blood with a particular antigen if their own blood does not have this antigen present. Concretely, blood is divided into four types: A, B, AB, and O. Patients with type A can receive blood types A or O; patients with type B can receive only B or O; patients with type O can receive only O, and patients with type AB can receive any of the four. Let sO, sA, sB, sAB denote the supply in whole units of the different blood types on hand. Assume that the hospital knows the projected demand for each blood type dO, dA, dB, dAB, in whole units, for the coming week. Describe how you can set up a bipartite graph with the following property: The maximum matching in the graph you create tells you if the blood supply on hand is sufficient to meet the projected demand. It is okay if your graph has a large number of vertices. Your description should include how many vertices you have, what they are, and what edges are present in your graph. You should also indicate why your graph is bipartite and what a perfect matching indicates in this grpah (in terms of the original problem statement).