The cost C (in dollars) of producing x units of a product isC= 1.70x + 9,000.(a) Find the average cost function C.C =(b) Find C when x = 1,000 and when x = 10,000.C(1,000) = $C(10,000)= $per unitper unit(c) Determine the limit of the average cost function as x approaches infinity.lim C(x) =X-00=Interpret the limit in the context of the problem.As more and more units are produced, the average cost per unit (in dollars) will approach $

Step 1: Average Cost FunctionThe average cost function, Ā(x), is the total cost divided by the…

Answered: The cost C (in dollars) of producing x…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.2: Domain And Range

Problem 61SE: The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is...

See similar textbooks

Similar questions

bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
2. -7 -6 -3 3 4 -2 -3 %24
Suppose that a software company produces CDs (computer disks) at a cost of $2 each, and fixed costs are $60. The cost function, the total cost of producing x disks, will then be C(x) = 2x + 50, and the average cost per unit will be the total cost divided by the number of units. (a) Find lim AC(x), which is the unit or marginal cost. lim AC(x)=L (b) Sketch the graph of AC(x), showing the horizontal asymptote. [Note: Your graph should be an illustration of the general business principle for linear cost functions: In the long run, average cost approaches marginal cost.] y 50 40 O 30 20 10 y 50 40 AC(x) = 30 - 2x + 60 20 10 10 10 20 20 30 30 40 40 50 A y 50 40 30 20 10 10 20 30 40 50 y 50 40 30 20 10 10 20 30 40
lim = e7x- e6x/ex-1 x>0
The price p (in dollars) and the demand x for a particular clock radio are related by the equation x=2000−20p. (A) Express the price p in terms of the demand x, and find the domain of this function. (B) Find the revenue R(x) from the sale of x clock radios. What is the domain of R? (C) Find the marginal revenue at a production level of 1200 clock radios. (D) Interpret R′(1600)=−60.00.
Suppose that a software company produces CDs (computer disks) at a cost of $4 each, and fixed costs are $50. The cost function, the total cost of producing x disks, will then be C(x) = 4x + 50, and the average cost per unit will be the total cost divided by the number of units. 4x + 50 AC(x) = (a) Find lim AC(x), which is the unit or marginal cost. x + c0 lim AC(x) = (b) Sketch the graph of AC(x), showing the horizontal asymptote. [Note: Your graph should be an illustration of the general business principle for linear cost functions: In the long run, average cost approaches marginal cost.]
A mixing vat initially contains 253 gallons of chemical A and 200 gallons of chemical B, mixed together. Inlet pumps are turned on at 7:00 a.m. (time t = 0) that pump in 3.7 gallons of chemical A each hour and 10.2 gallons of chemical B each hour, creating a constantly changing mix of the two chemicals over time. a. Write a function A(t) that gives the ratio of chemical A to chemical B after t hours of pumping. A(t) b. How many hours will it take for the ratio of chemical A to chemical B in the vat to reach 0.558? hours Round to three decimal places. c. Over a "long time," what value will the ratio of the amount of chemical A to the amount of chemical B get closer and closer to, if this mixing process is allowed to continue indefinitely? Round to three decimal places.
We encounter the composition h(T) = L(A(T)) with L and A defined as: A, the amount of ice stored in Arctic Glaciers (in tons) as a function of the average temeprature of the earth's surface T (in degrees Celsius) L, the difference in sea level since 2000 (in meters) as a function of the amount of ice stored in Arctic Glaciers (in tons) a) What is the sign of A'(T) at our current average temperature, 16.1 degrees Celsius? Explain briefly. b) What is the sign of L'(A) at our current amount of stored ice? Explain briefly. c) Write h'(16.1) using the chain rule. WHat is the sign of h'(16.1)?
f(x) = √x, a = 1
(x + h)³ = x³ h→000 ch bloow 46. lim
3x 1. Let g(x) = r-2 a. Compute lim, 9(x); - L b. Give equations of any horizontal and vertical asymptotes.

Recommended textbooks for you

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS