We all know the basic rule for blood donation: A patient of blood group A can receive only blood of group A or O$.$ A patient of blood group B can receive only blood of group A or O$.$ A patient of blood group O can receive only blood of group O$.$ A patient of blood group AB can receive blood of any group. 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 and dAB for the coming week. Give a polynomial time algorithm to evaluate if the blood on hand would suffice for the projected need. You should formulate this problem as a max$-$flow problem, establish a relation between the two problems by stating a theorem, and then you should prove the theorem.