Bipartite matching: A hospital has certain amounts of blood supply for each type of blood. One day a major accident happened and a large number of patients require blood transfusion. The blood types of the supply and of the patients are given in the table below. The rules for blood transfusion are the following: patients can always receive blood of the same type as their own; patients of type $AB$ can receive any type of blood; and any patient can receive type O blood. The problem is to determine whether the blood supply is sufficient, what additional supply is needed $($if any$),$ and how the blood supply should be used to allow transfusions for all patients.

$($a$)$ Describe in words how this can be transformed into a network flow problem.

You should state clearly what the vertices, edges and edge capacities are.

$($b$)$ Construct the network according to $($a$)$ for this particular example.

$($c$)$ Find the maximum flow and hence solve the blood transfusion problem

Make it hand written no Ai please