Question

World Foods,Inc.,. imports food products such as meats, cheese, and pastries to the United States from warehouses at ports in Hamburg, Marseilles, and Liverpool. Ships from these ports deliver the products to N New York, and Savannah, where they are stored in company warehouses before being shipped to distributior centers in Dallas, St. Louis, and Chicago. The products are then distributed to specialty food stores and sold through catalogs. The shipping costs ($/1,000 lb.) from the European ports to the U.S. cities and the available supplies (1,000 lb.) at the European ports are provided in the following table: U.S. City European Port 4. Norfolk 5. New York 6. Savannah Supply 1. Hamburg $420 $390 $610 55 2.Marseilles 510 590 470 78 3.Liverpool 450 360 480 37 The transportation costs ($/1,000 lb.) from each U.S. city of the three distdibution centers and the demands (1,000 Ib.) at the distribution centers are as follows: Distribution Center Warehouse 7. Dallas 8. St. Louis 9. Chicago $ 75 4. Norfolk 63 $81 5. New York 125 110 95 6. Savannah 68 82 95 Ib.)at the distribution centers are as follows: Distribution Center Warehouse 7. Dallas 8. St. Louis 9. Chicago 4. Norfolk 75 $63 $81 5. New York 125 110 95 6.Savannah 68 82 95 Demand 60 45 50 Determine the optimal shipments between the European ports and the warehouses and the distribution centers to minimize total transportation costs. At the optimal solution, how many shjpments are sent from Marselles to Savannah?

Answer 1

Set up the model as shown below

fx A1 K M RA A C D E G L N C O Norfolk New York Savannah Supply 1 Hamburg 420 390 610 55 Marseilles 510 59r 470 3 78 Liverpool 450 360 4 480 37 75 125 68 Dallas 5 60 6 63 45 110 82 St. Louis 7 50 81 95 95 Chicago Demand Norfolk New York Savannah Supply 10 Hamburg C 11 12 Marseilles 0 0 Liverpool 13 C 0 0 Dallas 14 C C 15 St, Louis Chicago 16 O 0 0 Demand 17 18 19 Flow in C 0 Flow out C 20 21 22 Cost 0 23 24 Sheet1213 Sheet1215 Sheet1217 Sheet1218 Sheet1212 Sheet1214 Sheet1216 4 1566 READY

The excel formulas are shown below

f A1 H G E D C A Supply Savannah New York Norfolk 55 610 390 420 Hamburg 2 78 470 590 510 Marseilles 2 37 480 360 450 Liverpool 4 Dallas 68 125 75 60 St. Louis 82 110 63 6 45 Chicago 95 95 81 7 50 Demand Supply -SUM(B11:D11) -SUM (B12 :D12) -SUM (B13: D13) Savannah New York Norfolk 10 Hamburg 11 0 C Marseilles 12 Liverpool 13 Dallas C 14 SUM(B14:D14) St. Louis C C 15 SUM(B15:D15) Chicago 0 C 16 SUM(B16:D16) Demand 17 18 SUM(D11:D13) SUM(D14:D16) =SUM(C11:C13) SUM(C14:C16) SUM(B11:B13) =SUM(B14:B16) Elow in 19 Flow out 20 21 -SUMPRODUCT(B2:D7,B11:D16) Cost 22 23 24 Sheet1218 Sheet1217 Sheet1216 Sheet1215 Sheet1213 Sheet1214 1190 . Sheet1212 4 READY

The solver parameters are shown below

fx Solver Parameters A D E G H R Norfolk New York Savannah Supply 1 Set Objective: SB$22 Hamburg 390 55 2 420 610 3 Marseilles 510 590 470 78 To: O Max Value Of C Min Liverpool 4 450 360 480 37 Changing Variable Cells: 60 75 125 68 Dallas 5 SBS11:SD$16 63 110 82 St. Louis 6 45 95 Chicago 7 50 81 95 Subject to the Constraints SAS14-SA$16 -SAS5:SAS7 Demand Add Change Norfolk New York Savannah Supply 10 11 Hamburg Delete 12 Marseilles 0 Liverpool 13 C 0 Reset Al Dallas 14 0 C 0 Load/Save 15 0 0 0 St. Louis Make Unconstrained Variables Non-Negative 16 Chicago Select a Solving Method: Simplex LP 17 Demand Options 18 Solving Method 19 Flow in C 0 Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that 20 Flow out C e non-smooth. 21 22 0 Cost Help Solve Close 23 24 .. Sheet1213 Sheet1215 Sheet1217 Sheet1218 Sheet1212 Sheet1214 Sheet1216 4 E ENTER

The result is shown below. The answer is 77362

fx A1 RA K M A C D E G N C Norfolk New York Savannah Supply 1 Hamburg 420 390 610 55 Solver Results Marseilles 59C 470 3 510 78 Liverpool 450 360 4 480 37 All Constraints and optimali conditions are catiefied 75 125 68 Dallas 60 Reports 6 63 45 110 82 St. Louis Answer O Keep Solver Solution Sensitivity 7 81 95 95 Chicago 50 Limits Demand O Restore Original Values Return to Solver Parameters Dialog Outline Reports Norfolk New York Savannah Supply 10 Hamburg 55 11 42 13 0 Save Scenario. OK Cancel 12 Marseilles 0 63 63 13 Liverpool C 37 0 37 Solver found a solution. All Constraints and optimality conditions are 14 60 60 Dallas satisfied. least a local optimal Elobal 4т St. Louis When the GRG engine is used, Solver has found implex 15 45 O 3 means Solver has fou s used, thi 50 Chicago 16 50 0 optimal solution 17 Demand 18 19 Flow in 50 63 42 Flow out 42 50 63 20 21 77362 22 Cost 23 24 Sheet1212 Sheet1213 Sheet1214 Sheet1215 Sheet1216 Sheet1217 Sheet1218 READY 159% -