| Los AvailabilityWhitewater Canos Duras (bbl) | Kingsport | 12 15 17 35 | Danville | 14 9 10 26 | Macon | 13 20 11 42 | SelmaColumbus | 17 16 19 537 14 12 29 | AllentownCapacity(barrels) | 22 16 18 3865 80 105 |

Math Tutorial 1
Lil-Help.com

1. I treat this problem similar to a transportation problem for optimization. In this case we want to find routes which will minimize the cost of transportation of the 6 plants to the 3 waste disposal sites. The following table represents cost and capacity.

for the above table let,

quantity of waste transported from the plant to the waste center, where

hence we want to minimize the objective function

which is subject to the following constraints,

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| White water | LosCanos | Duras | Kingport | 35 | | | Danville | | | 26 | Macon | | | 42 | Selma | 1 | 52 | | Columbus | 29 | | | Allentown | | 28 | 10 | Dummy | | | 27 |

Math Tutorial 2
Lil-Help.com

2. Using the excel solver gives the following results,

In words I would transport,

35 bbl from Kingport to Whitewater

1 bbl from Selma to Whitewater

29 bbl from Columbus to Whitewater

52 bbl from Selma to Los Canos

28 bbl from Allentown to Los Canos

26 bbl from Danville to Duras

42 bbl from Macon to Duras

10 bbl from Allentown to Duras

this gives the following cost for the objective function,

hence, $2822 is the minimum transportation cost.

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AlternateRoute | Plant | Intermediary | Disposalcentre | Cost | Minimumcost | 1 | Kingsport | | Duras | $17 | $15 | | Kingsport | Danville | Duras | $15 | | 2 | Macon | | Los Canos | $20 | $19 | | Macon | Selma | Los Canos | $19 | | 3 | Selma | | White water | $17 | $10 | | Selma | Columbus | White water | $10 | | 4 | Selma | | Duras | $19 | $14 | | Selma | Macon | Duras | $14 | | 5 | Allentown | | White water | $22 | $20 | | Allentown | Kingsport | White water | $20 | | 6 | Allentown | | Duras | $18 | $17 | | Allentown | Danville | Duras | $17 | | | Los AvailabilityWhitewater Canos Duras (bbl) | Kingsport | 12 15 15 35 | Danville | 14 9 10 26 | Macon | 13 19 11 42 | SelmaColumbus | 10 16 14 537 14 12 29 | AllentownCapacity(barrels) | 20 16 17 3865 80 105 |

Math Tutorial 3
Lil-Help.com

3. There are certain routes which are advantageous in this situation and will lower cost even more.
These routes are given in the following table,

Hence, there are six alternate routes through which the cost is less. This gives a new transportation model given in the following table,

For the new model, the objective function is as follows,

and the constraints,

All products provided by Lil-Help are intended for academic resource and research only. These are not designed to replace student personal work and rules and regulations from schools, colleges, and universities should be applied when using our services. Customers are responsible for understanding and adhering to plagiarism rules and Lil-Help is not responsible for inappropriate use of products.

| White water | LosCanos | Duras | Kingport | | 16 | 19 | Danville | | 26 | | Macon | | | 42 | Selma | 36 | | 17 | Columbus | 29 | | | Allentown | | 38 | | Dummy | | | 27 |

Math Tutorial 4
Lil-Help.com

using the excel solver,

and the minimum cost is,

5. After a mathematical analysis using optimization techniques, it is clear that the minimum cost is
$2822. This is based on having no intermediaries. If intermediaries are allowed, the price drops to
$2630. In order to achieve such a cost the company must use the following routes for transportation:
Kingsport takes 19 bbl to Duras goes to Danville first, and then from Danville to Duras. 36 bbl waste from Shelma to Whitewater goes to Columbia first and then to Whitewater. Finally, 17 bbl going from
Shelma to Duras must be transported to Macon first and then to Duras.

All products provided by Lil-Help are intended for academic resource and research only. These are not designed to replace student personal work and rules and regulations from schools, colleges, and universities should be applied when using our services. Customers are responsible for understanding and adhering to plagiarism rules and Lil-Help is not responsible for inappropriate use of products.

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