Question 1136931
Let {{{ y }}} = attendance in thousands
Let {{{ x }}} = ticket price in dollars
-----------------------------------------
You are given 2 points on a straight line:
( 11, 28 )
( 9, 34 )
Use point-slope formula
{{{ ( y - 28 ) / ( x - 11 ) = ( 34 - 28 ) / ( 9 - 11 ) }}}
{{{ ( y - 28 ) / ( x - 11 ) = 6/(-2) }}}
{{{  ( y - 28 ) / ( x - 11 ) = -3 }}}
{{{ y - 28 = -3*( x - 11 ) }}}
{{{ y - 28 = -3x + 33 }}}
{{{ y = -3x + 61 }}}
------------------------
check:
( 11,28 )
{{{ 28 = -3*11 + 61 }}}
{{{ 28 = -33 + 61 }}}
{{{ 28 = 28 }}}
OK
( 9,34 )
{{{ 34 = -3*9 + 61 }}}
{{{ 34 = -27 + 61 }}}
{{{ 34 = 34 }}}
OK
------------------------
Revenue, {{{R}}} = [ ticket price ] x [ attendance ]
{{{ R = x*( -3x + 61 ) }}}
{{{ R = -3x^2 + 61x }}}
{{{ x[max] = -b/(2a) }}}
{{{ x[max] = -61/( 2*(-3)) }}}
{{{ x[max] = 61/6 }}
{{{ x[max] = 10.17 }}}
------------------------------
{{{ R[max] = ( 61/6 )*( -3*(61/6) + 61 ) }}}
{{{ R[max] = 10.1667*( -30.5 + 61 ) }}}
{{{ R[max] = 10.1667*30.5 }}}
{{{ R[max] = 310.0843 }}}
$310,084
If you need to, get a 2nd opinion also
--------------------------------------
Here's the plots of {{{ y }}} and {{{ R }}}
 {{{ graph( 400, 400, -5, 30, -10, 70, -3x + 61  ) }}} 
{{{ graph( 400, 400, -5, 30, -40, 400, -3x^2 + 61x ) }}}