2. A company manufactures USB drives. The daily cost in dollars of producing x USB drives is given by the function C(x) = -0.03x? + 10x +54 where 0sxS 300. a) Write the marginal cost function. b) What is the value of the marginal cost at a production level of 100 USB drives per day? c) Interpret your answer to part (b) in context of the problem. d) Write the average cost function C (x). e) Find C(100) and interpret your answer in the context of the problem.
2. A company manufactures USB drives. The daily cost in dollars of producing x USB drives is given by the function C(x) = -0.03x? + 10x +54 where 0sxS 300. a) Write the marginal cost function. b) What is the value of the marginal cost at a production level of 100 USB drives per day? c) Interpret your answer to part (b) in context of the problem. d) Write the average cost function C (x). e) Find C(100) and interpret your answer in the context of the problem.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### USB Drive Manufacturing Cost Analysis
#### Problem Statement
A company manufactures USB drives. The daily cost in dollars of producing \( x \) USB drives is given by the function:
\[ C(x) = -0.03x^2 + 10x + 54 \]
where \( 0 \leq x \leq 300 \).
#### Tasks
1. **Marginal Cost Function**
a) Write the marginal cost function.
2. **Marginal Cost Value at Specific Production Level**
b) What is the value of the marginal cost at a production level of 100 USB drives per day?
3. **Interpretation of the Marginal Cost**
c) Interpret your answer to part (b) in the context of the problem.
4. **Average Cost Function**
d) Write the average cost function \( \overline{C}(x) \).
5. **Average Cost at Specific Production Level**
e) Find \( \overline{C}(100) \) and interpret your answer in the context of the problem.
#### Explanation
1. **Marginal Cost Function**
To find the marginal cost function, we need to differentiate the cost function \( C(x) \):
\[ C(x) = -0.03x^2 + 10x + 54 \]
Taking the derivative with respect to \( x \):
\[ C'(x) = \frac{d}{dx}(-0.03x^2 + 10x + 54) \]
\[ C'(x) = -0.06x + 10 \]
Therefore, the marginal cost function is \( C'(x) = -0.06x + 10 \).
2. **Marginal Cost at 100 USB Drives**
To find the marginal cost at \( x = 100 \):
\[ C'(100) = -0.06(100) + 10 \]
\[ C'(100) = -6 + 10 \]
\[ C'(100) = 4 \]
The value of the marginal cost at a production level of 100 USB drives per day is $4.
3. **Interpretation of Marginal Cost**
The marginal cost of $4 means that for each additional USB drive produced after reaching 100 USB drives per](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84552427-9a89-4a6a-8bce-a48127de447f%2F277acc0d-3bee-42c6-87f9-7c6218563fe5%2F7m66qcl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### USB Drive Manufacturing Cost Analysis
#### Problem Statement
A company manufactures USB drives. The daily cost in dollars of producing \( x \) USB drives is given by the function:
\[ C(x) = -0.03x^2 + 10x + 54 \]
where \( 0 \leq x \leq 300 \).
#### Tasks
1. **Marginal Cost Function**
a) Write the marginal cost function.
2. **Marginal Cost Value at Specific Production Level**
b) What is the value of the marginal cost at a production level of 100 USB drives per day?
3. **Interpretation of the Marginal Cost**
c) Interpret your answer to part (b) in the context of the problem.
4. **Average Cost Function**
d) Write the average cost function \( \overline{C}(x) \).
5. **Average Cost at Specific Production Level**
e) Find \( \overline{C}(100) \) and interpret your answer in the context of the problem.
#### Explanation
1. **Marginal Cost Function**
To find the marginal cost function, we need to differentiate the cost function \( C(x) \):
\[ C(x) = -0.03x^2 + 10x + 54 \]
Taking the derivative with respect to \( x \):
\[ C'(x) = \frac{d}{dx}(-0.03x^2 + 10x + 54) \]
\[ C'(x) = -0.06x + 10 \]
Therefore, the marginal cost function is \( C'(x) = -0.06x + 10 \).
2. **Marginal Cost at 100 USB Drives**
To find the marginal cost at \( x = 100 \):
\[ C'(100) = -0.06(100) + 10 \]
\[ C'(100) = -6 + 10 \]
\[ C'(100) = 4 \]
The value of the marginal cost at a production level of 100 USB drives per day is $4.
3. **Interpretation of Marginal Cost**
The marginal cost of $4 means that for each additional USB drive produced after reaching 100 USB drives per
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