Ex 3.4 Q8 Marginal Average Cost for Producing LCD TVs Find the average cost function C associated with the following total cost function C given in dollars.C(x) = 0.000008x³ -0.02x² + 110x + 45,000C(x) =(a) What is the marginal average cost function C' (in dollars)?C'(x) =(b) Compute the following values. (Round your answers to three decimal places.)C'(5,000)(10,000)==

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Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

Section: Chapter Questions

Problem 8PS

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Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.
The demand function for the Viking Boat’s 34-ft Sundancer yacht isp = 200 − 0.01x ln x,where x denotes the number of yachts and p is the price per yacht in hundreds of dollars.(a) Find the revenue function and the marginal revenue function for this model of yacht.(b) Use the result of part (a) to estimate the revenue realized from the sale of the 500-th34-ft Sundance yacht. (Note: This is an estimate, so be careful to use the correct functionfrom part (a) and to evaluate it at the correct value of x.)(c) Now compute the exact revenue realized from the sale of the 500-th 34-ft Sundance yacht. (d) Comment on the approximation provided in part (b).
The cost (in dollars) of producing x units of a certain commodity is given below. C(x) = 7000 + 14x + 0.15x2(a) Find the average rate of change of C with respect to x when the production is changed from x = 100 to the given value. (i) x = 103$ per unit(ii) x = 101$ per unit (b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.)$ per unit
The cost (in dollars) of producing x units of a certain commodity is C(x) = 8000 + 12x + 0.05x2. A. Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.) B. Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.)
Marginal Cost Suppose the monthly total cost for themanufacture of golf balls is C(x)= 3450 + 0.56x,where x is the number of balls produced each month.a. What is the slope of the graph of the total costfunction?b. What is the marginal cost (rate of change of thecost function) for the product?c. What is the cost of each additional ball that is produced in a month?
The cost (in dollars )of producing x units of a certain commodity is given below C(x) = 9000+ 12x +0.15x^2 A) find the average rate of the change of c with respect to x when the production is changed from x = 100 to the given value . I) x=105 $____ Per unit ii) X=101 $___ per unit B) find the instantaneous rate of change of c with respect to x when = 100 . This is called the marginal cost ) $___ per unit
A company has found that the marginal cost of a new production line (in thousands) is C'(x)=(9/x+e), where x is the number of years the line is in use. Find the total cost function for the prodcution lin (in thousands). The fixed cost is $20,000.
The total cost of producing x units of a certain commodity is given by C(x) = 20x ^ 2 + 100 a)Find the marginal cost function. b). Find the average cost function
The cost (in dollar ) of producing x units of a certain commodity is given below . C(x) =9000+11x +01x^2 A) Find the average value of the rate change of c with respect to x and when the production is changed from x =100 to the given value . I) x= 102 $___ per unit ii) x= 101 $ ____ per unit B) find the instantaneous rate of change to c with respect to when x = 100 . ( this is called marginal cost ) $____ per unit
Consider a cost function C(x) given by C(x)=10,000+20x. Calculate the marginal average cost when x=500, use the result to approximate the total cost when x=501, and calculate the percentage error between your approximation and the exact result. Give your answer as a percentage to 4decimal places. Do not include the percent symbol in your answer.
A company's cost function is C(x) = 16x2 + 900 dollars, where x is the number of units. Find the marginal cost function. MC(x) = Evaluate it at x = 10
A manufacturer estimates that the cost of producing x items is C(x) = 250 + 3x + 0.001x2 a. Find the average cost function and the marginal cost for x = 1000. b. Find the value of x for which the average cost is smallest. c. What can you say about the marginal cost at the point where the average cost is smallest?

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