Question 188911
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The <i>x</i>-coordinate of the vertex of a parabola whose equation is in the form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x) = ax^2 + bx + c]


is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_V = \frac{-b}{2a}]


For your given function,


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R(p) = -p^2 + 1900p]


<i>a</i> = -1 and <i>b</i> = 1900, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ p_V = \frac{-1900}{2(-1)} = 950]


Hence the unit price to maximize revenue is $950.  Less than a thousand dollars for a new heavy duty John Deere tractor?  Is someone nuts?  Fire the marketing guy who came up with that revenue function.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R(p) = -p^2 + 190000p]


giving a max revenue price of $95,000 - that I might believe.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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