Chapter 14.2, Problem 54E

Work the following marginal productivity problems. (See Example 6.)

A manufacturer estimates that production (in hundreds of units) is a function of the respective amounts x and y of labor and capital used, as follows:

$f\left(x,y\right)=\left[\frac{1}{2}{x}^{-1/3}+\frac{2}{3}{y}^{-1/3}\right].$

Find the number of units produced when 27 units of labor and 64 units of capital are utilized.

Find and interpret $f_x\left(27,64\right)$ and $f_y\left(27,64\right)$

What would be the approximate effect on production of increasing labor by 1 unit?

What would be the approximate effect on production of increasing capital by 1 unit?