MAT 540 Week 10

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MAT540 Homework Week 10

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MAT540

Week 10 Homework

Chapter 6 1. Consider the following transportation problem:

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

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

computer.

2. Consider the following transportation problem:

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:

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

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:

Warehouse Distribution Center

MAT540 Homework Week 10

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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.

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:

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.