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so let me talk about the other way to solve this problem so one way to solve this problem is just think straight about inputs okay the other is to think about a two-step problem very similar to how we approach the consumers problem is step one lets minimize cost for a given output and step two is to pick the output to maximize profits everybody understand it so thats going to be our our process one first were going to minimize cost for a given output and then were going to choose the level of output to maximize profits okay how do we do that well the first problem I think we already know how to do first step is minimize the sum of the X I WI subject to f of X 1 up to xn equals y weve seen that problem before right for this part of the problem theres absolutely no distinction between consumer theory and production theory right because were fixing the output and whether youre fixing utility or fixing the level of output of the firm doesnt really matter in either case were minim