Optimization of Three Crops

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= C_AA_A + C_BA_B + C_CA_C + β_ABA_AA_B + β_ACA_AA_C + β_BCA_BA_C 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 A_B first to acquire how many acres of Crop B would be allowed.

After I found A_B I then took the partial derivative with respect to A_C 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 A_A+A_B+A_C=23 from which I was able to attain A_A 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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