C(x) = 4,500 + 30x + 0.2x² en the average cost of producing x items is represented by the following equation. total cost 4,500 C(x) = + 30 + 0.2x (a) Find the instantaneous rate of change of average cost with respect to the number of units produced, at any level of pro (b) Find the level of production at which this rate of change equals zero. X = (c) At the value found in part (b), find the instantaneous rate of change of cost and find the average cost. instantaneous rate of change of cost

Essentials of Business Analytics (MindTap Course List)
2nd Edition
ISBN:9781305627734
Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson
Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson
Chapter13: Nonlinear Optimization Models
Section: Chapter Questions
Problem 2P: The Cobb-Douglas production function is a classic model from economics used to model output as a...
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Suppose that the total cost function, in dollars, for the production of x units of a product is given by the equation shown below.
C(x) = 4,500 + 30x + 0.2x²
Then the average cost of producing x items is represented by the following equation.
total cost
4,500
C(x)
+ 30 + 0.2x
(a) Find the instantaneous rate of change of average cost with respect to the number of units produced, at any level of production.
(b) Find the level of production at which this rate of change equals zero.
X =
(c) At the value found in part (b), find the instantaneous rate of change of cost and find the average cost.
instantaneous rate of change of cost
average cost
What do you notice?
Transcribed Image Text:Suppose that the total cost function, in dollars, for the production of x units of a product is given by the equation shown below. C(x) = 4,500 + 30x + 0.2x² Then the average cost of producing x items is represented by the following equation. total cost 4,500 C(x) + 30 + 0.2x (a) Find the instantaneous rate of change of average cost with respect to the number of units produced, at any level of production. (b) Find the level of production at which this rate of change equals zero. X = (c) At the value found in part (b), find the instantaneous rate of change of cost and find the average cost. instantaneous rate of change of cost average cost What do you notice?
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