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Assume the Cobb-Douglas production function $f(x, y)=16200 x^{\frac{1}{5}} y^{\frac{4}{5}}$, where $x$ is the number of units of labor, and $y$ is the number of units of capital. If each unit of labor costs $\$ 8,$ each unit of capital $\$ 243,$ and the production level of 80,000 units is to be achieved, (a) determine the number of units of labor and capital that minimize the cost. (b) Find the minimum cost.

(a) $(25,800 / 243)$(b) $\$ 1,000$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 5

Economic Applications

Partial Derivatives

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Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

04:14

03:34

Use the method of Lagrange…

02:32

The production of a compan…

05:11

A consulting firm for a ma…

02:53

The research department of…

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