International Paper Company has four warehouses at different cities: Buffalo, De
ID: 447118 • Letter: I
Question
International Paper Company has four warehouses at different cities: Buffalo, Detroit, Pittsburgh and Raleigh. They provide paper to five book publishers in Boston, New York, Chicago, Indianapolis and Memphis.
The costs of shipping one box of paper, the amount of paper (in boxes) available at each warehouse, and the amount of paper ordered (in boxes) by each publisher are found in the table below:
From / To
Boston
New York
Chicago
I ndianapolis
Memphis
Supply
Buffalo
9
7
11
12
13
700
Detroit
12
11
10
10
8
1000
Pittsburgh
11
9
9
10
10
1300
Raleigh
6
5
9
8
7
1400
Demand
500
1400
1100
800
600
Find the amounts to Ship from the following Warehouses to Publishers with the goal of Minimizing Transportation Costs
From / To
Boston
New York
Chicago
I ndianapolis
Memphis
Supply
Buffalo
9
7
11
12
13
700
Detroit
12
11
10
10
8
1000
Pittsburgh
11
9
9
10
10
1300
Raleigh
6
5
9
8
7
1400
Demand
500
1400
1100
800
600
Explanation / Answer
Formulating a Linear Program
Objective function = Minimize Sumproduct of ( Product allocation across area, Transport costs to each location )
Minimum Trasnportation Cost = 33700
From/ To
Product allocation
From/ To
Subject to Constraints
Demand in Boston = 500
Demand in NewYork = 1400
Demand in Chicago = 1100
Demand in Indianapolis = 800
Demand in Memphis = 600
Supply in Buffalo <= 700
Supply in Detroit <= 1000
Supply in Pittsburgh <= 1300
Supply in Raleigh <= 1400
Transportation MatrixFrom/ To
Boston New York Chicago Indianapolis Memphis Supply Buffalo 9 7 11 12 13 700 Detroit 12 11 10 10 8 1000 Pittsburgh 11 9 9 10 10 1300 Raleigh 6 5 9 8 7 1400 Demand 500 1400 1100 800 600Related Questions
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