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Using Linear Programming to find optimal builds in League of Legend

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due to how LP solvers work, we can't just find a solution where the variables are real numbers, and then round those up to get an integer. constructing the solution is easy: we call the minimise function on the cost expression and provide a default solver, since we don't have a preference about which one we use. there might also be other builds that cost a bit more gold, but that scale significantly better into the late game, or that include items that provide stronger passive effects, or that are better in specific match-ups.

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