Question 927621
When the form of the equation is
{{{ f(x) = a*x^2 + b*x + c }}}, the
value of {{{ x }}} where f(x) is a maximum
occurs at {{{ -b/(2a) }}}
------------------------
{{{ r(p) = -2.5p^2 + 550p }}}
{{{ p[max] = -550/(-2.5*2) }}}
{{{ p[max] = 550/5 }}}
{{{ p[max] = 110 }}}
(a) 
At a price of $110 the revenue is maximized
-----------------
(b)
{{{ r(p) = -2.5p^2 + 550p }}}
{{{ r[max] = -2.5*110^2 + 550*110 }}}
{{{ r[max] = -30250 + 60500 }}}
{{{ r[max] = 30250 }}}
The maximum revenue is $30,250
--------------------------------
Here's a plot:
{{{ graph( 400, 400, -50, 250, -10000, 35000, -2.5x^2 + 550x ) }}}