Marriage Example

Four women, Alice, Barbara, Cathy and Daniele, and four men, Eric, Frank, George and Harry, decide that they are all going to get married. The problem is they can't decide who is going to marry whom. They decide that each couple will rank, on a scale of 0 to 10, how happy they would be together. Compute the set of marriages that maximizes the total happiness.
Alice Barbara Cathy Daniele
Eric 10 5 8 10
Frank 2 8 6 5
George 7 8 3 9
Harry 2 4 6 10