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Strayer University MAT540 – Quantitative Methods

September 1, 2011

Stateline Shipping and Transport Company

In Excel, or Other Suitable Program, Develop a Model for Shipping the Waste

Directly from the 6 Plants to the 3 Waste Disposal Sites The Stateline Shipping and Transport Company wanted to transport chemical wastes from the six plants to the three waste disposal sites. The six pants and their capacity for wastes generated are shown below. Also shown are the three waste disposal sites and their demand requirements.

|Plants |Supply (barrels) |

|1. Kingsport |35 |

|2. Danville |26 |

|3. Macon |42 |

|4. Selma |53 |

|5. Columbus |29 |

|6. Allentown |38 |

|Waste Disposal Sites |Demand (barrels) |

|A. Whitewater |65 |

|B. Los Canos |80 |

|C. Duras |105 |

Shown below are the shipping costs ($/bbl) from each waste disposal site to each plants.

|Plants |Waste Disposal Sites |

| |A. Whitewater |B. Los Canos |C. Duras |

|1. Kingsport |$12 |$15 |$17 |

|2. Danville |14 |9 |10 |

|3. Macon |13 |20 |11 |

|4. Selma |17 |16 |19 |

|5. Columbus |7 |14 |12 |

|6. Allentown |22 |16 |18 |

Mathematical Formulation The objective of the problem is to develop a shipping schedule that minimizes the total cost of transportation. The objective function Z represents the cost. In this transportation model the decision variables, Xij, represent the quantity of waste transported from the i-th plant (where i=1,2,3,4,5,6) to the j-th waste disposal site (where j= A,B,C). The linear programming model for this problem can be written as follows. minimize Z=$12X1A+15X1B+17X1C+14X2A+9X2B+10X2C+13X3A+20X3B+11X3C + 17X4A+16X4B+19X4C+7X5A+14X5B+12X5C+22X6A+16X6B+18X6C subject to

X1A+X1B+X1C = 35

X2A+X2B+X2C = 26

X3A+X3B+X3C = 42

X4A+X4B+X4C = 53

X5A+X5B+X5C = 29

X6A+X6B+X6C = 38

X1A+X2A+X3A+X4A+X5A+X6A

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