(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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Consider the region below f(x) = (11-x), above the x-axis, and between x = 0 and x = 11. Let x; be the midpoint of the ith subinterval. Complete parts a. and b. below. a. Approximate the area of the region using eleven rectangles. Use the midpoints of each subinterval for the heights of the rectangles. The area is approximately square units. (Type an integer or decimal.)

Rama/Shutterstock.com Romaset/Shutterstock.com The power station has three different hydroelectric turbines, each with a known (and unique) power function that gives the amount of electric power generated as a function of the water flow arriving at the turbine. The incoming water can be apportioned in different volumes to each turbine, so the goal of this project is to determine how to distribute water among the turbines to give the maximum total energy production for any rate of flow. Using experimental evidence and Bernoulli's equation, the following quadratic models were determined for the power output of each turbine, along with the allowable flows of operation: 6 KW₁ = (-18.89 +0.1277Q1-4.08.10 Q) (170 - 1.6 · 10¯*Q) KW2 = (-24.51 +0.1358Q2-4.69-10 Q¹²) (170 — 1.6 · 10¯*Q) KW3 = (-27.02 +0.1380Q3 -3.84-10-5Q) (170 - 1.6-10-ºQ) where 250 Q1 <1110, 250 Q2 <1110, 250 <3 < 1225 Qi = flow through turbine i in cubic feet per second KW = power generated by turbine i in kilowatts

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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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