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Coalco produces coal at three mines and ships it to four customers. The cost per ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons) for each mine are given in Table 1. The number of tons of coal demanded by each customer is given in Table 2. The cost (in dollars) of shipping a ton of coal from a mine to each customer is given in Table 3. It is required that the total amount of coal shipped contains at most 5% ash and at most 4% sulfur.

Coalco produces coal at three mines and ships it to four customers. The cost per ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons) for each mine are given in Table 1. The number of tons of coal demanded by each customer is given in Table 2. The cost (in dollars) of shipping a ton of coal from a mine to each customer is given in Table 3. It is required that the total amount of coal shipped contains at most 5% ash and at most 4% sulfur.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 61P
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Linear programming formulation. 

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Coalco produces coal at three mines and ships it to four customers. The cost per ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons) for each mine are given in Table 1. The number of tons of coal demanded by each customer is given in Table 2. The cost (in dollars) of shipping a ton of coal from a mine to each customer is given in Table 3. It is required that the total amount of coal shipped contains at most 5% ash and at most 4% sulfur. Formulate a linear programming (LP) model that minimizes the cost of meeting customer demands. Table 1: Properties of coal from different mines Production cost Сараcity Ash content Sulfur content Mine 1 $50 120 0.08ton 0.05ton Mine 2 $55 100 0.06ton 0.04ton Mine 3 $62 140 0.04ton 0.03ton Table 2: Demand from each customer Customer 1 Customer 2 Customer 3 Customer 4 80 70 60 90 Table 3: Cost (in dollars) from each mine to each customer Customer 1 Customer 2 Customer 3 Customer 4 Mine 1 4 6. 8 12 Mine 2 9. 6. 7 11 Mine 3 8 12 3
Transcribed Image Text:Coalco produces coal at three mines and ships it to four customers. The cost per ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons) for each mine are given in Table 1. The number of tons of coal demanded by each customer is given in Table 2. The cost (in dollars) of shipping a ton of coal from a mine to each customer is given in Table 3. It is required that the total amount of coal shipped contains at most 5% ash and at most 4% sulfur. Formulate a linear programming (LP) model that minimizes the cost of meeting customer demands. Table 1: Properties of coal from different mines Production cost Сараcity Ash content Sulfur content Mine 1 $50 120 0.08ton 0.05ton Mine 2 $55 100 0.06ton 0.04ton Mine 3 $62 140 0.04ton 0.03ton Table 2: Demand from each customer Customer 1 Customer 2 Customer 3 Customer 4 80 70 60 90 Table 3: Cost (in dollars) from each mine to each customer Customer 1 Customer 2 Customer 3 Customer 4 Mine 1 4 6. 8 12 Mine 2 9. 6. 7 11 Mine 3 8 12 3
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ISBN:
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