The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula C(x) = 100 + 41x − 0.04x2. (a) Find the marginal cost function C'(x). C'(x) = ___________ Use it to determine how fast the cost is going up (in $) at a production level of 100 teddy bears. $ ________ per teddy bear Compare this with the exact cost of producing the 101st teddy bear (in $). The cost is increasing at a rate of $ _____ per teddy bear. The exact cost of producing the 101st teddy bear is $ ________ . Thus, there is a difference of $ ___________ .
The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula C(x) = 100 + 41x − 0.04x2. (a) Find the marginal cost function C'(x). C'(x) = ___________ Use it to determine how fast the cost is going up (in $) at a production level of 100 teddy bears. $ ________ per teddy bear Compare this with the exact cost of producing the 101st teddy bear (in $). The cost is increasing at a rate of $ _____ per teddy bear. The exact cost of producing the 101st teddy bear is $ ________ . Thus, there is a difference of $ ___________ .
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Question
The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula
C(x) = 100 + 41x − 0.04x2.
(a) Find the marginal cost function C'(x).
C'(x) = ___________
Use it to determine how fast the cost is going up (in $) at a production level of 100 teddy bears.
$ ________ per teddy bear
Compare this with the exact cost of producing the 101st teddy bear (in $).
The cost is increasing at a rate of $ _____ per teddy bear. The exact cost of producing the 101st teddy bear is $ ________ . Thus, there is a difference of $ ___________ .
(b)Find the average cost function C, and evaluate C(100) (in $).
C(x)= _______
What does the answer tell you?
The average cost of producing the first hundred teddy bears is $ _________ per teddy bear.
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