(a) To find: The objective function if the steel manufacturer that can produce P ( K , L ) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C ( K , L ) dollars. The available budget is $ 800 , 000 . The maximum production achieved is 10 , 000 with the use of $ 550 , 000 capital and $ 150 , 000 of the labor. The value of the Langrage multiplier is λ = 0.0125 .

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Answer 1

Question

Chapter 8.6, Problem 24P

To determine

(a)

To find:

The objective function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(b)

To find:

The constraint function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(c)

To find:

The unit of λ if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(c)

To find:

The practical meaning of the statement λ=0.0125 if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

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Students have asked these similar questions

the quantity, q, of a product manufactures depends on the number of workers.W , and the amount of capital invested, K, and is represented by the Cobb-Douglasfunctionq = 64W^3/4 K^1/4 .Suppose further that labor costs $18 per worker and capital costs $28 per unit, and thebudget is $4600. Let λ be the Lagrange multiplier. Does increasing the budget by $1 allow theproduction of λ extra units of the product? Explain why as shown in the image below..

1. How much are three numbers worth if you want their product to be maximum and their sum to be 1000? Use Lagrange multipliers to get your answer or show that it is not possible

Hello, I asked a similar question and the answer was quite helpful, but I have a followup. How do I find the local maxima of the function f(x,y) = 1 + x^2 + y^2 - 4xy with a constraint g(x,y) = x^2 + y^3 - 2 = 0? Using the Lagrange multiplier method the previous answer helped me get to the minima, but since the answer is one point only, how do I find the maxima?

Answer 2

Question

Chapter 8.6, Problem 24P

To determine

(a)

To find:

The objective function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(b)

To find:

The constraint function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(c)

To find:

The unit of λ if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(c)

To find:

The practical meaning of the statement λ=0.0125 if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

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Answer 3

Question

Chapter 8.6, Problem 24P

To determine

(a)

To find:

The objective function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(b)

To find:

The constraint function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(c)

To find:

The unit of λ if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(c)

To find:

The practical meaning of the statement λ=0.0125 if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

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Answer 4

Question

Chapter 8.6, Problem 24P

To determine

(a)

To find:

The objective function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(b)

To find:

The constraint function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(c)

To find:

The unit of λ if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(c)

To find:

The practical meaning of the statement λ=0.0125 if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

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Answer 5

Chapter 8.6, Problem 24P

To determine

(a)

To find:

The objective function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(b)

To find:

The constraint function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(c)

To find:

The unit of λ if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

To determine

(c)

To find:

The practical meaning of the statement λ=0.0125 if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

Answer 6

Chapter 8.6, Problem 24P

To determine

(a)

To find:

The objective function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

Answer 7

Chapter 8.6, Problem 24P

To determine

(a)

To find:

The objective function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

Answer 8

To determine

(b)

To find:

The constraint function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

Answer 9

To determine

(b)

To find:

The constraint function if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

Answer 10

To determine

(c)

To find:

The unit of λ if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

Answer 11

To determine

(c)

To find:

The unit of λ if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

Answer 12

To determine

(c)

To find:

The practical meaning of the statement λ=0.0125 if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

Answer 13

To determine

(c)

To find:

The practical meaning of the statement λ=0.0125 if the steel manufacturer that can produce P(K,L) tons of the steel with the use of K units of the capital and L units of the labor, with the production cost being C(K,L) dollars. The available budget is $800,000. The maximum production achieved is 10,000 with the use of $550,000 capital and $150,000 of the labor. The value of the Langrage multiplier is λ=0.0125.

Answer 14

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Answer 15

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Answer 16

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Answer 17

Ch. 8.1 - Prob. 1P Ch. 8.1 - Prob. 2P Ch. 8.1 - Prob. 3P Ch. 8.1 - Prob. 4P Ch. 8.1 - Prob. 5P Ch. 8.1 - Prob. 6P Ch. 8.1 - Prob. 7P Ch. 8.1 - Prob. 8P Ch. 8.1 - Prob. 9P Ch. 8.1 - Prob. 10P

Solution Summary: The author explains the objective function of a steel manufacturer that can produce P(K,L) tons of steel with the use of K units of the capital and L units

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Chapter 8 Solutions