Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 30 days

Continue

Input your name and email to request the answer

Like

Report

Assume the Cobb-Douglas production function $f(x, y)=10000 x^{\frac{1}{4}} y^{\frac{3}{4}}$, where $x$ is the number of units of labor, and $y$ is the number of units of capital. If each unit of labor costs $\$ 27,$ each unit of capital $\$ 16,$ and the production level of 540,000 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) (16,81)(b) $\$ 1728$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 5

Economic Applications

Partial Derivatives

Missouri State University

Harvey Mudd College

University of Nottingham

Idaho State University

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…

02:53

The research department of…

No transcript available

View More Answers From This Book

Find Another Textbook

03:02

Evaluate $\int_{R} \int f(x, y) d A$ for $R$ and $f$ as given.(a) $f(x, …

02:01

Find and classify, using the second partial derivative test, the critical po…

02:05

Evaluate the given integral.$$\int\left(3 x^{5}+1\right)^{8} 15 x^{4} d …

03:15

Evaluate the given integral.$$\int x^{n} \ln (x) d x$$

04:38

(a) determine the average value of the given function over the given interva…

09:45

Find the partial derivatives with respect to (a) $x,$ (b) $y$ and (c) $z$.

Evaluate the given integral and check your answer.$$\int\left(4 x^{3}-9 …

02:08

Determine the area of the region between the given curves.$$f(x)=-4 x^{2…

02:22

Evaluate the given integral and check your answer.$$\int \frac{4 x^{3}-7…

02:00