$10x^{\frac{1}{3}}{y}^{\frac{2}{3}}=120$

$(a)$ Find $\frac{dy}{dx}.$

$\frac{dy}{dx}=$

Evaluate $\frac{dy}{dx}at$ the point $(27,8).(Round$ your answer $to$ four decimal places.$)$

$(b)$ Interpret the result $of$ part $(a).$

When

$is$ spent $on$ labor and

$---$Select$---$

$is$ spent $on$ capital, the amount spent $on$ capital with respect $to$ the amount spent $on$ labor $is$

$--$Select$---$

$.$