manuracturer's total production of a new product is P(L, K) = 1800L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $200, a unit of capital $800, and the total budget for labor and capital is $960,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? %24 (b) Find the value of the Lagrange multiplier.
manuracturer's total production of a new product is P(L, K) = 1800L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $200, a unit of capital $800, and the total budget for labor and capital is $960,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? %24 (b) Find the value of the Lagrange multiplier.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Topic Video
Question
100%
![A manufacturer's total production of a new product is
P(L, K) = 1800L2/3K1/3
where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $200, a unit of capital $800, and the total budget for labor and capital is
$960,000.
(a) To maximize production, how much should be spent on labor?
2$
How much on capital?
24
(b) Find the value of the Lagrange multiplier.
Give an interpretation of the Lagrange multiplier.
O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in labor, L, by one unit.
O The Lagrange multiplier is the approximate increase in the total budget for labor and capital resulting from an increase in the optimal value of P by one unit.
O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in the total budget for labor and capital by one unit.
O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in capital, K, by one unit.
O The Lagrange multiplier is the approximate increase in capital, K, resulting from an increase in the optimal value of P by one unit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbdb7cc2c-0afb-45df-a4d0-29e6ebad7bac%2Fe374f54d-7119-4bfb-87e3-86de865c75a9%2F1vszu0b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A manufacturer's total production of a new product is
P(L, K) = 1800L2/3K1/3
where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $200, a unit of capital $800, and the total budget for labor and capital is
$960,000.
(a) To maximize production, how much should be spent on labor?
2$
How much on capital?
24
(b) Find the value of the Lagrange multiplier.
Give an interpretation of the Lagrange multiplier.
O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in labor, L, by one unit.
O The Lagrange multiplier is the approximate increase in the total budget for labor and capital resulting from an increase in the optimal value of P by one unit.
O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in the total budget for labor and capital by one unit.
O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in capital, K, by one unit.
O The Lagrange multiplier is the approximate increase in capital, K, resulting from an increase in the optimal value of P by one unit.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)