### Projects (1999 - Spring 2008)

Engineering >> Civil & Environmental Engineering

## by Alyssa Domek

Submitted : Fall 2011

This project was proposed to help a farmer fully optimize all three of his crops to gain the most profit without exceeding his 23 acre limit. For this project to be successfully addressed I took note of all the given information from the problem and made sure to record every formula correctly. From there I plugged in the given information into the main formula of Profit= CAAA + CBAB + CCAC + βABAAAB + βACAAAC + βBCABAC where I was left with two unknowns. After plugging in other given information that will be explained soon, I then took the partial derivative with respect to AB first to acquire how many acres of Crop B would be allowed.

After I found AB I then took the partial derivative with respect to AC from which I was able to obtain the total acres of Crop C that would be allowed. From there I proceeded to insert my answers into the equation AA+AB+AC=23 from which I was able to attain AA and establish the number of acres of Crop A the farmer would be allowed to plant to achieve the maximum profit. To check my work I proved that I calculated the maximum acreage by solving the determinant matrix and I concluded that I was correct.

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 Advisors : Masahiko Saito, Mathematics and Statistics Scott Campbell, Chemical & Biomedical Engineering Suggested By : Scott Campbell