# We have 3 Factories, 3 Warehouses, and 4 Stores Factories Montgomery St. Louis Flagstaff Supply 26,000.00 32,000.00 19,000.00 Warehouses Cincinnati Seattle Denver Stores Baltimore Los Angeles Orlando Minneapolis Demand 9,500.00 23,000.00 16,000.00 26,500.00 Shipping Costs Baltimore 45.00 Denver Orlando Cincinnati \$23.00 52.00 Cincinnati Los Angeles Minneapolis Orlando Denve \$29.00 \$23.00 \$47.00 \$62.00 Cincinnati Denver Los Angeles Orlando Flagstaff \$50.00 \$17.00 \$27.00 \$88.00 Cincinnati Orlando Los Angeles Denver Montgomery \$46.00 \$24.00 S39.00 \$40.00 Los AngelesMinneapolis Baltimore \$86.00 Seattle \$29.00 \$71.00 Cincinnati Denver Seattle St. Louis \$19.00 \$30.00 S58.00 https://d2vlcm61l7u1fs.cloudfront.net/media%2F9e5%2F9e55dcc4-1d81-45f7-9df3-255f11d6b415%2FphpPqlXuy.png

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

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