question 6

Question

A producer of graphing calculators has found that the revenue R (in dollars) is well represented by the expression below when the unit price is set at "x" dollars. If the producer sets the calculator price to earn maximum revenue, what will be this maximum revenue? Type in your answer as a whole number only. Do not type the dollar symbol or any letters with your answer, just the numerical value. R(x)=-4x^2+1320x

Answer 1

R(x) = -4x² + 1320x

 

This is a quadratic equation of the form ax² + bx + c, where a = -4, b = 1320, and c = 0.  The graph is a parabola. Since a<0, the parabola opens downward with the vertex at the top.  The vertex is thus the maximum value, representing the maximum revenue (R).

 

The x coordinate of the vertex of a parabola if always located at the point x = -b/2a.  Plug in the values for a and b from your equation to find x.  Then plug the x-coordinate of the vertex into the revenue equation to find the maximum revenue.