Question 4788
This equation represents a parabola that opens downward, so the vertex of the parabola will be the point at which maximum revenue occurs.  As in the last question that I posted, the vertex occurs at x = {{{(-b) /(2a)}}}, where a = coefficient of {{{x^2}}} and b = coefficient of x.  In this case a= -0.01 and b= 800.  


Maximum revenue occurs at {{{x=(-b)/(2a) = (-800)/(2*(-0.01))= 800/0.02 }}}= 40,000 units.

To find the maximum revenue, substitute x= 40,000 into the original equation for R and it turns out that {{{R = 800*40000 - 0.01*40000^2}}} or $16,000,000.  


R^2 at SCC