Complete the following problems from Chapter 6: Problems 4, 6, 36, 48
4. Consider the following transportation problem:
To (cost)
From 1 2 3 Supply
A $ 6 $ 9 $100 130
B 12 3 5 70
C 4 8 11 100
Demand 80 110 60
Formulate this problem as a linear programming model and solve it by using the computer.
6. Consider the following transportation problem:
To (cost)
From 1 2 3 Supply
A $ 6 $ 9 $ 7 130
B 12 3 5 70
C 4 8 11 100
Demand 80 110 60
Solve it by using the computer.
36. World Foods, Inc., imports food products such as meats, cheeses, and pastries to the United States from warehouses at ports in Hamburg, Marseilles, and Liverpool. Ships from these ports deliver the products to Norfolk, New York, and Savannah, where they are stored in company warehouses before being shipped to distribution 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 distribution centers and the demands (1,000 lb.) 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.
The Omega pharmaceutical firm has five salespersons, whom the firm wants to assign to five sales regions. Given their various previous contacts, the salespersons are able to cover the regions in different amounts of time. The amount of time (days) required by each salesperson to cover each city is shown in the following table:
Region (days)
Salesperson A B C D E
1 17 10 15 16 20
2 12 9 16 9 14
3 11 16 14 15 12
4 14 10 10 18 17
5 13 12 9 15 11
Which salesperson should be assigned to each region to minimize total time? Identify the optimal assignments and compute total minimum time.