College Algebra

Question

A manager has determined that the revenue R(x) (in millions of dollars) made on the sale of supercomputers is given by R(x)= 48x - 3x^2, where x represents the number of supercomputers sold. How many supercomputers must be sold to maximize revenue? According to this model, what is the maximum revenue (in millions of dollars)?

Answer 1

The graph of the revenue function is a parabola opening downward.  The maximum occurs at the vertex.  The x-coordinate of the vertex of a parabola with equation y = Ax²+Bx+C is x = -B/(2A).

 

So, for the given equation, the x-coordinate of the vertex is                  x = -48/(2(-3)) = 8

 

Therefore, to maximize revenue, sell 8 supercomputers

 

  Maximum Revenue = R(8) = 48(8) - 3(8)²

 

                                       = $192,000,000