MAT540 Quantitative Methods Week 10 Homework Complete Solution

Question: #1203

MAT540 Homework Week 10
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

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.