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The overall conclusion will be the following:

{{quotation|The absolute (i.e., global) maximum for profit must occur either at one of these three points: zero quantity of production, the maximum quantity of production, or some local maximum at an intermediate quantity of production. In the last case, that ''must'' be a point where <math>MR = MC</math> and, more specifically, the value <math>MR - MC</math> is changing sign from positive to negative. Here, <math>MR</math> and <math>MC</math> denote respectively the marginal revenue and marginal cost.}}

To jump directly to the meat of the analysis, see the [[#Formal mathematical analysis|formal mathematical analysis section]].

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