I am a high school student trying to work on a math project. I have plotted the coordinates of all households in a Kenyan village and am trying to locate the geometric median of the set of points to find the ideal point to built a well.
I have tried using Fermat's problem and the smallest enclosing circle problem, but these solutions are too complex for my high school math project. Is there a way to solve this using high school calculus? It could go a little beyond but I can't do things like second-order cone optimization.
The idea is to find an equation for the total distance to the well (unweighted). Take the points (1,2), (1,-1), (-2,-1) so that there are 3 households in the village. I found the distance equation, but realized that there are 2 variables in the equation so I can't do optimization and implicit differentiation.
I don't know what to do! I am already halfway through this project and can't scrap it!