MAT540
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 ($/1,000 lb.) from the European ports to the U.S. cities and the
available supplies (1000 lb.) at the European ports are provided in the
following table:
MAT540 Homework
Week 10
Page 2 of 2
From
To (Cost)
Supply
4.
Norfolk
5. New York
6. Savannah
1.
Hamburg
320
280
555
75
2.
Marseilles
410
470
365
85
3.
Liverpool
550
355
525
40
The
transportation costs ($/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.
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