The shortest travel distance is 16, attained by the carrier taking the following stops: A $\rightsquigarrow B_{2} \rightsquigarrow C_{2} \rightsquigarrow B_{1} \rightsquigarrow B_{3} \rightsquigarrow C_{3} \rightsquigarrow C_{1}.$ There are two slightly different routes with the same length of 16: Route 1: 2(A) $\rightarrow 6 \rightarrow 7(B_{2}) \rightarrow 8 \rightarrow 11(C_{2}) \rightarrow 8 \rightarrow 3(B_{1}) \rightarrow 4(B_{3}) \rightarrow 15 \rightarrow 14 \rightarrow 13(C_{3}) \rightarrow 12(C_{1}).$ Route 2: 2(A) $\rightarrow 6 \rightarrow 7(B_{2}) \rightarrow 10 \rightarrow 11(C_{2}) \rightarrow 8 \rightarrow 3(B_{1}) \rightarrow 4(B_{3}) \rightarrow 15 \rightarrow 14 \rightarrow 13(C_{3}) \rightarrow 12(C_{1}).$