The long-run average cost AC(x) can be approximated by a quadratic function. Find the minimum long-run average cost (LRAC) by finding the vertex of AC(x) and sketch the graph, given

(1) Here, with a > 0, the parabola opens up.

(3) With the parabola opening up from the vertex (60, 500), the graph does not cross the x axis. See Fig. 3-27. To see how similar problems can also be solved by the method of completing the square, see Dowling, Schaum’s Outline of Calculus for Business, Economics, and the Social Sciences, Problems 3.33 to 3.35.

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AC (x) = x-120x + 4100