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What if I told you that when you press solve in excel, you're really just drawing a bunch of lines on a graph and finding where they intersect?
Well, that's basically what Simplex is. Maximization in excel is based on algorithmic matrix algebra, formally called Gauss-Jordan Elimination. The easiest way to understand Gauss-Jordan elimination is to do it, but I'm going to do my best to save you the pain. In essence, to find an optimization solution, one must simultaneously solve a system of equations where the number of equations is equal to the number of variables.
So, let's say we have an objective function, Z,
where, Z = 10x + 5y.