Question 1092291
{{{ P = ( 100 + 20n )*( 120 - 5n ) }}}
{{{ P = 12000 + 2400n - 500n - 100n^2 }}}
{{{ P = -100n^2 + 1900n + 12000 }}}
The formula for the n-value of the vertex is
{{{ n[max] = -b/(2a) }}}
{{{ n[max] = -1900 / (2*(-100)) }}}
{{{ n[max] = 9.5 }}}
and, also
{{{ P[max] = -100*9.5^2 + 1900*9.5 + 12000 }}}
{{{ P[max] = -100*90.25 + 18050 + 12000 }}}
{{{ P[max] = -9025 + 30050 }}}
{{{ P[max] = 21025 }}}
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The best price to charge is:
{{{ 100 + 20n = 100 + 20*9.5 }}}
{{{ 100 + 20n = 290 }}}
$290 per vehicle
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Here's the plot:
{{{ graph( 700, 400, -2, 25, -25, 250, -x^2 + 19x + 120 ) }}} 
The P-values are all divided by {{{ 100 }}}
Definitely try to get another opinion if needed