(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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The chief economist for Argus Corporation, a large appliance manufacturer, estimated the firm’s short-run cost function for vacuum cleaners using an average variable cost function of the form AVC = a + bQ + cQ2 where AVC = dollars per vacuum cleaner and Q = number of vacuum cleaners produced each month. Total fixed cost each month is $180,000. The following results were obtained: DEPENDENT VARIABLE: AVC R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 19 0.7360 39.428 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 191.93 54.65 3.512 0.0029 Q -0.0305 0.00789 23.866 0.0014 Q2 0.0000024 0.00000098 2.449 0.0262 c) If Argus Corporation produces 8,000 vacuum cleaners per month, what is the estimated average variable cost?

E3

An open-top box with a square base is made with 1200 cm2 of cardboard. A. Express the area A = 1200 of the box as a function of the base side x and the height h. 1200 = B. Express the volume Vof the box as a function of the base x only. V(z) = C. Find the dimensions of the box that maximize its volume, and the largest volume. I = cm h = cm V. cm3

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