Graph Algorithms · Challenge problem

A town's possible roads among intersections $A$–$F$ are $AB{:}3, AC{:}6, BC{:}2, BD{:}5, CD{:}4, CE{:}7, DE{:}3, DF{:}8, EF{:}2$. The town wants road $CE$ built no matter what, in addition to connecting every intersection as cheaply as possible otherwise. What is the minimum total cost of a road network that includes $CE$?