Graph Algorithms · Superchallenge problem

A cable company must connect warehouses $A,B,C,D,E$. Possible direct cables and costs are $AB{:}3, AC{:}5, AD{:}7, AE{:}9, BC{:}2, CD{:}4, DE{:}3, BE{:}8, CE{:}6$. For reliability, warehouse $A$ must end up with EXACTLY $2$ direct cables in the final network (not $1$, not $3$ or more). What is the minimum total cost of such a network connecting all five warehouses?