https://d2vlcm61l7u1fs.cloudfront.net/media%2F169%2F169ae95a-37a5-4cfa-95a8-449e4ca64202%2FphpoauHkX.png
Formula:
G2 =SUMIF($A$2:$A$22,F2,$C$2:$C$22)-SUMIF($B$2:$B$22,F2,$C$2:$C$22) copy to G2:G11
I13 =SUMPRODUCT(D2:D22,C2:C22)
The optimal solution is following
Flow indicates the number of units to transported From source node To destination node
From To Flow
Cincinnati Denver 0
Cincinnati Orlando 0
Cincinnati Baltimore 9500
Denver Cincinnati 0
Denver Los Angeles 0
Denver Minneapolis 26500
Denver Orlando 0
Flagstaff Cincinnati 0
Flagstaff Denver 6000
Flagstaff Los Angeles 13000
Flagstaff Orlando 0
Montgomery Cincinnati 0
Montgomery Orlando 16000
Montgomery Los Angeles 10000
Montgomery Denver 0
Seattle Los Angeles 0
Seattle Minneapolis 0
Seattle Baltimore 0
St. Louis Cincinnati 9500
St. Louis Denver 20500
St. Louis Seattle 0
Total cost = 3,695,500