Question 453695
Let {{{ M }}} = money taken in
Let {{{ i }}} = number of $1 increases
Money in = (number of adult visitors) x (admission per visitor)
{{{ M = ( 300 - 15i )*( 10 + i ) }}}
{{{ M = 3000 - 150i + 300i - 15i^2 }}}
{{{ M = -15i^2 + 150i + 3000 }}}
{{{ M = -i^2 + 10i + 200 }}}
The maximum money in occurs at {{{ i = -b/(2a) }}}
where the equation has the form {{{ f(x) = a*x^2 + bx + c }}}
{{{ a = -1 }}}
{{{ b = 10 }}}
{{{ i[max] = -10/(2*(-1)) }}}
{{{ i[max] = 5 }}}
{{{ 10 + i = 10 + 5 }}}
{{{ 10 + i = 15 }}}
The most profitable admission price is $15/visitor