The cost, in dollars, of producing x yards of a certain fabric is C(x) = 1100 + 13x − 0.1x2 + 0.0005x3. (a) Find the marginal cost function. C'(x) = (b) Find C'(500) and explain its meaning. What does it predict? C'(500) = and this is the rate at which costs are increasing with respect to the production level when x = . C'(500) predicts the cost of producing the ---Select--- 499th 501st 401st 599th 500th yard. (c) Compare C'(500) with the cost of manufacturing the 501st yard of fabric. (Round your answers to four decimal places.) The cost of manufacturing the 501st yard of fabric is C(501) − C(500) = − 45,100 ≈ , which is approximately C'(500).
The cost, in dollars, of producing x yards of a certain fabric is C(x) = 1100 + 13x − 0.1x2 + 0.0005x3. (a) Find the marginal cost function. C'(x) = (b) Find C'(500) and explain its meaning. What does it predict? C'(500) = and this is the rate at which costs are increasing with respect to the production level when x = . C'(500) predicts the cost of producing the ---Select--- 499th 501st 401st 599th 500th yard. (c) Compare C'(500) with the cost of manufacturing the 501st yard of fabric. (Round your answers to four decimal places.) The cost of manufacturing the 501st yard of fabric is C(501) − C(500) = − 45,100 ≈ , which is approximately C'(500).
Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter4: Extent (how Much) Decisions
Section: Chapter Questions
Problem 9MC
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Question
The cost, in dollars, of producing x yards of a certain fabric is
C(x) = 1100 + 13x − 0.1x2 + 0.0005x3.
(a) Find the marginal cost function.
(b) Find
(c) Compare
C'(x) =
(b) Find
C'(500)
and explain its meaning. What does it predict?
C'(500) =
and this is the rate at which costs are increasing with respect to the production level when
x = . C'(500)
predicts the cost of producing the ---Select--- 499th 501st 401st 599th 500th yard.(c) Compare
C'(500)
with the cost of manufacturing the 501st yard of fabric. (Round your answers to four decimal places.)
The cost of manufacturing the 501st yard of fabric is
C(501) − C(500) = − 45,100 ≈ ,
which is approximately
C'(500).
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