The cost in dollars for a company to produce x widgets is given by C(x)=4250 +6x for ≥0, and the price demand function, in dollars per widget, is p(x)=25-0.02x for 0≤x≤2250 a. the profit function is a quadratic function and so its graph is a parabola. does the parabola open up or down? b. find the vertex of the profit function P(x) c. state the maximum profit and the number of widgets which yield the maximum profit  d. determine the price to charge per widget in order to maximize profit e. find and interpret the break even points

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.