R(x) = 312x0.2x^2 = 0.2x^2+312x. This is the graph of a parabola. To find the # of units x that produce the maximum revenue for this function, we can find the equation for the axis of symmetry. As any parabola can be written in the forn ax^2+bx+c, the axis of symmetry is x= b/2a. In this case, x= (312)/2(0.2) = 312/0.4 = 780. Therefore
780 units produce the maximum revenue, which is R(780)= 312(780) 0.2(780)^2 =
121680 dollars.
8/23/2014

Jimmy E.