# quantitative methods 2

MAT540 Week 10 Homework

Chapter 6 1. Consider the following transportation problem:

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

2. Consider the following transportation problem:

MAT540 Homework Week 10 Page 1 of 2

 From To (cost) Supply 1 2 3 A \$5 \$4 \$3 130 B 2 3 5 70 C 4 8 7 100 Demand 80 110 60
 From To (cost) Supply 1 2 3 A \$5 \$ 12 \$2 130 B 2 9 5 70 C 4 24 7 100 Demand 80 110 60

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:

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:

 From To (cost) Supply 4. Norfolk 5. New York 6. Savannah 1. Hamburg \$420 \$390 \$610 55 2. Marseilles 510 590 470 78 3. Liverpool 450 360 480 37
 Warehouse Distribution Center

MAT540 Homework Week 10 Page 2 of 2

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 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:

 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
 Region (days) Sales- person 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.