### Projects (1999 - Spring 2008)

Engineering >> Mechanical Engineering

## by Emily Dutton

Submitted : Fall 2011

The goal of this project was to determine the minimum cost for laying a pipeline that went through land and water. Given that the pipeline in the water cost double the amount of pipeline through land, I had to find the optimal pipe placement to minimum cost. First, I started by finding the equations of lines and distance formulas that varied as the pipe orientation changed. I used these formulas to formulate a cost function which is equal to the total cost of the pipeline construction. By taking the derivatives, I found the critical points, which are the exact coordinates of the pipeline at minimum cost. To prove that these critical points are a local minimum, I used the second derivative test. My conclusions that I made is that the pipeline ascends up to the first coast line, continues in a straight line across the water, and then reaches the other land with a mirror image of the first line. This is the exact route that I pictured before I started the project, but I had to find the exact coordinates and make sure the solution was mathematically correct.

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 Advisors : Gerald Hefley, Mathematics and Statistics Scott Campbell, Chemical & Biomedical Engineering Suggested By : Scott Campbell