MAT540
Week 10 Homework
Chapter 6

Consider the following transportation problem:
From 
To (cost) 
Supply 

1 
2 
3 

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.

Consider the following transportation problem:
From 
To (cost) 
Supply 

1 
2 
3 

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.

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 

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.
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