The total cost (in dollars) of producing x food processors is C(X)=2400+90x-0.2x2. (A) Find the exact cost of producing the 91st food processor. (B) Use the marginal cost to approximate the cost of producing the 91st food processor. (A) The exact cost of producing the 91st food processor is $ (B) Using the marginal cost, the approximate cost of producing the 91st food processor is $
The total cost (in dollars) of producing x food processors is C(X)=2400+90x-0.2x2. (A) Find the exact cost of producing the 91st food processor. (B) Use the marginal cost to approximate the cost of producing the 91st food processor. (A) The exact cost of producing the 91st food processor is $ (B) Using the marginal cost, the approximate cost of producing the 91st food processor is $
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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![### Cost Analysis of Producing Food Processors
The total cost (in dollars) of producing \( x \) food processors is \( C(x) = 2400 + 90x - 0.2x^2 \).
To analyze the costs, consider the following tasks:
#### (A) Find the Exact Cost of Producing the 91st Food Processor
Calculate the total cost of producing the first 91 food processors and then subtract the total cost of producing the first 90 food processors. Specifically, find:
\[ C(91) - C(90) \]
#### (B) Use the Marginal Cost to Approximate the Cost of Producing the 91st Food Processor
The marginal cost at \( x = 90 \) is given by \( C'(x) \), the derivative of the total cost function \( C(x) \). Calculate:
\[ C'(x) = \frac{d}{dx}[2400 + 90x - 0.2x^2] \]
Then evaluate \( C'(90) \) to approximate the cost of producing the 91st food processor.
### Questions
1. **(A)** The exact cost of producing the 91st food processor is $_______.
2. **(B)** Using the marginal cost, the approximate cost of producing the 91st food processor is $_______.
> **Note:** Enter your answer in each of the answer boxes.
This content is designed to guide students in solving for both the exact and approximate costs associated with incremental production using calculus-based methods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5403b22d-6bfd-443b-9939-b04fac993812%2F1fb8c8ae-7f46-4161-97e1-2af203e284b2%2Fw1wlj1y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Cost Analysis of Producing Food Processors
The total cost (in dollars) of producing \( x \) food processors is \( C(x) = 2400 + 90x - 0.2x^2 \).
To analyze the costs, consider the following tasks:
#### (A) Find the Exact Cost of Producing the 91st Food Processor
Calculate the total cost of producing the first 91 food processors and then subtract the total cost of producing the first 90 food processors. Specifically, find:
\[ C(91) - C(90) \]
#### (B) Use the Marginal Cost to Approximate the Cost of Producing the 91st Food Processor
The marginal cost at \( x = 90 \) is given by \( C'(x) \), the derivative of the total cost function \( C(x) \). Calculate:
\[ C'(x) = \frac{d}{dx}[2400 + 90x - 0.2x^2] \]
Then evaluate \( C'(90) \) to approximate the cost of producing the 91st food processor.
### Questions
1. **(A)** The exact cost of producing the 91st food processor is $_______.
2. **(B)** Using the marginal cost, the approximate cost of producing the 91st food processor is $_______.
> **Note:** Enter your answer in each of the answer boxes.
This content is designed to guide students in solving for both the exact and approximate costs associated with incremental production using calculus-based methods.
![### Understanding Limits using Graphs
#### Refer to the graph of \( y = f(x) \) to the right to describe the behavior of \( \lim_{x \to 3^-} f(x) \). Use \( -\infty \) and \( \infty \) where appropriate.
**Instructions**: Select the correct choice below and fill in any answer boxes in your choice.
1. \( \lim_{x \to 3^-} f(x) = \) [ _____ ]
2. The limit does not exist and is neither \( -\infty \) nor \( \infty \).
**Graph Description**:
The graph represents a function \( f(x) \) on a coordinate plane with \( x \)-axis ranging from -10 to 10 and \( y \)-axis ranging from -10 to 10. The function shows a vertical asymptote at \( x = 3 \), indicating the function approaches infinity as \( x \) approaches 3 from the left. This is evident as the curve heads upwards steeply near \( x = 3 \).
The possible choices are:
- **A**. \( \lim_{x \to 3^-} f(x) = \boxed{\infty} \)
- **B**. The limit does not exist and is neither \( -\infty \) nor \( \infty \).
The correct answer will be:
- **A**. \( \lim_{x \to 3^-} f(x) = \boxed{\infty} \)
---
**Course**: \( \text{MA2300-Calculus for Business and Economics, Summer 2021} \) based on Barnett: College \(\ldots\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5403b22d-6bfd-443b-9939-b04fac993812%2F1fb8c8ae-7f46-4161-97e1-2af203e284b2%2F3x67mqe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Limits using Graphs
#### Refer to the graph of \( y = f(x) \) to the right to describe the behavior of \( \lim_{x \to 3^-} f(x) \). Use \( -\infty \) and \( \infty \) where appropriate.
**Instructions**: Select the correct choice below and fill in any answer boxes in your choice.
1. \( \lim_{x \to 3^-} f(x) = \) [ _____ ]
2. The limit does not exist and is neither \( -\infty \) nor \( \infty \).
**Graph Description**:
The graph represents a function \( f(x) \) on a coordinate plane with \( x \)-axis ranging from -10 to 10 and \( y \)-axis ranging from -10 to 10. The function shows a vertical asymptote at \( x = 3 \), indicating the function approaches infinity as \( x \) approaches 3 from the left. This is evident as the curve heads upwards steeply near \( x = 3 \).
The possible choices are:
- **A**. \( \lim_{x \to 3^-} f(x) = \boxed{\infty} \)
- **B**. The limit does not exist and is neither \( -\infty \) nor \( \infty \).
The correct answer will be:
- **A**. \( \lim_{x \to 3^-} f(x) = \boxed{\infty} \)
---
**Course**: \( \text{MA2300-Calculus for Business and Economics, Summer 2021} \) based on Barnett: College \(\ldots\)
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