The Cobb$-$Douglas production function for $an$ automobile manufacturer $is$

$f(x,y)=100x^{0\mathrm{.}6}{y}^{0\mathrm{.}4}$

where $xis$ the number $of$ units $of$ labor and $yis$ the number $of$ units $of$ capital. Estimate the average production level when the number $of$ units $of$ labor $x$ varies between $500$

and $550$ and the number $of$ units $of$ capital $y$ varies between $225$ and $250.(Round$ your answer $to$ two decimal places.$)$