# Math_HL_IA - Farmland Optimization Matthew Simpson Period 3...

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Farmland OptimizationMatthew SimpsonPeriod 3
IntroductionI chose to research the optimization of farmland for my Internal Assessment for several reasons. First, I knew that I wanted my project to have something to do with calculus because I have always found myself fascinated with the ways that it can be applied to find solutions to real world problems. One aspect of calculus that stood out to me while narrowing down the math category for my topic was optimization where derivatives are used to calculate the optimal dimensions of a certain shape. Because of my fascination with efficiency, I typically strive to complete or accomplish things in the most productive way. I am always aspiring to find more efficient ways to do things every day in my life because finding more effective methods results in more getting done. Naturally, this concept can be applied to nearly any practical situation. As I considered some of the many applications for optimization of an area, I came to think about what I was learning about in one of my favorite classes- Environmental Science. In Environmental Science we had been discussing the effects of drastic population growth on the Earth, a topic that I found captivating. I took a special interest in this topic because of how many variables that were to be considered with population growth and the abundance of ways to combat the adverse impacts that population has on the environment. We had been learning about sustainability and its relationship with crop demand and population growth. As we learned aboutthe consequences of inefficient use of land leading to low production and more waste, I began to make connections between agriculture and the application of calculus. Since many ways of increasing agricultural efficiency requires chemicals and genetically modifying crops, people are reluctant to employ these methods. This is because people are generally wary of things that have been modified by science because they do not understand what they are consuming. In addition
to this, many efficiency boosting methods result in decreased productivity over long periods of time because of soil exhaustion or increased susceptibility to crop disease. In this research project, I intend to examine how to figure out the dimensions that would provide the maximum area and crop yield for a given plot of land. In doing this, it will be easier