Assume that it costs a company approximately C(x) = 700,000 + 250x + 0.0004x2 dollars to manufacture x game systems in an hour. (a) Find the marginal cost function, and use it to estimate how fast the cost is increasing when x = 60,000. Compare this with the exact cost of producing the 60,001st game system. (b) Find the average cost function C(x) and the average cost to produce the first 60,000 game systems. (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 60,000 game systems.
Assume that it costs a company approximately C(x) = 700,000 + 250x + 0.0004x2 dollars to manufacture x game systems in an hour. (a) Find the marginal cost function, and use it to estimate how fast the cost is increasing when x = 60,000. Compare this with the exact cost of producing the 60,001st game system. (b) Find the average cost function C(x) and the average cost to produce the first 60,000 game systems. (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 60,000 game systems.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.1: Quadratic Functions
Problem 6SC: A company that makes and sells baseball caps has found that the total monthly cost C in dollars of...
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Question
Assume that it costs a company approximately
C(x) = 700,000 + 250x + 0.0004x2
dollars to manufacture x game systems in an hour.
(a)
Find the marginal cost function, and use it to estimate how fast the cost is increasing when x = 60,000. Compare this with the exact cost of producing the 60,001st game system.
(b)
Find the average cost function
C(x)
and the average cost to produce the first 60,000 game systems.(c)
Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 60,000 game systems.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Consider the cost of a company,
To calculate the marginal cost of the function,
Hence the marginal cost of the given function is 250+0.0008x
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