MAT 540 Week 10 Homework Chapter 6

1. Consider the following transportation problem:

From To (Cost) Supply 1 2 3 A 6 5 5 150 B 11 8 9 85 C 4 10 7 125 Demand 70 100 80

Formulate this problem as a linear programming model and solve it by the using the computer.

2. Consider the following transportation problem:

From To (Cost) Supply 1 2 3 A 8 14 8 120 B 6 17 7 80 C 9 24 10 150 Demand 110 140 100 Solve it by using the computer.

3. 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 foods stores and sold through catalogs. The shipping costs ($/1,000 lb.) from the European ports to the U.S. cities and the available supplies (1000 lb.) at the European ports are provided in the following table: From To (Cost) Supply 4. Norfolk 5. New York 6. Savannah 1. Hamburg 320 280 555 75 2. Marseilles 410 470 365 85 3. Liverpool 550 355 525 40

The transportation costs ($/1000 lb.) from each U.S. city of the three distribution centers and the demands (1000 lb.) at the distribution centers are as follows:

Warehouse Distribution Center 7. Dallas 8. St. Louis 9. Chicago 4. Norfolk 80 78 85 5. New York 100 120 95 6. Savannah 65 75 90 Demand 85 70 65 Determine the optimal shipments between the European ports and the warehouses and the distribution centers to minimize total transportation costs.

4. The Omega Pharmaceutical firm has five salespersons, whom the firm wants to assign to five sales regions. Given their various previous contacts, the sales persons 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:

Salesperson Region (days) A B C D E 1 20 10 12 10 22 2 14 10 18 11 15 3 12 13 19 11 14 4 16 12 14 22 16 5 12 15 19 26 23 Which salesperson should be assigned to each region to minimize total time? Identify the optimal assignments and compute total minimum time.