The dollar cost of producing x bagels is C(x) = 300 + 0.25x – 0.6(- 1000 Determine the cost of producing 3000 bagels. (Use decimal notation. Give your answer to one decimal place.) C(3000) = $ %3D Estimate the cost of the 3001st bagel. (Use decimal notation. Give your answer to three decimal places.)
The dollar cost of producing x bagels is C(x) = 300 + 0.25x – 0.6(- 1000 Determine the cost of producing 3000 bagels. (Use decimal notation. Give your answer to one decimal place.) C(3000) = $ %3D Estimate the cost of the 3001st bagel. (Use decimal notation. Give your answer to three decimal places.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![### Calculating Production Costs for Bagels
#### Cost Function
The dollar cost of producing \( x \) bagels is given by the function:
\[ C(x) = 300 + 0.25x - 0.6 \left( \frac{x}{1000} \right)^3 \]
#### Questions to Solve
1. **Determine the Cost of Producing 3000 Bagels**
Using the given cost function, we need to calculate the cost for \( x = 3000 \) and provide the answer to one decimal place.
\[ C(3000) = \$ \]
2. **Estimate the Cost of the 3001st Bagel**
To estimate the cost of producing the 3001st bagel, consider the incremental cost by examining the derivative if necessary and provide the answer to three decimal places.
\[ \text{Cost of the 3001st bagel} = \$ \]
#### Steps to Solve
1. **Substitute \( x = 3000 \) into the cost function**
\[ C(3000) = 300 + 0.25(3000) - 0.6 \left( \frac{3000}{1000} \right)^3 \]
2. **Simplify the Expression**
Calculate each term step-by-step to find the total cost.
3. **For the 3001st Bagel**
Approximate the marginal cost by differentiating \( C(x) \) and evaluating at \( x = 3000 \), or calculate \( C(3001) - C(3000) \).
#### Providing the Answers
Make sure to present your final answers clearly with the appropriate decimal precision as requested in the questions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7369c9e1-cd27-40fa-b19e-4e793313e403%2F20167401-d532-40b0-9a92-e137701e5d53%2Fw2jy918.png&w=3840&q=75)
Transcribed Image Text:### Calculating Production Costs for Bagels
#### Cost Function
The dollar cost of producing \( x \) bagels is given by the function:
\[ C(x) = 300 + 0.25x - 0.6 \left( \frac{x}{1000} \right)^3 \]
#### Questions to Solve
1. **Determine the Cost of Producing 3000 Bagels**
Using the given cost function, we need to calculate the cost for \( x = 3000 \) and provide the answer to one decimal place.
\[ C(3000) = \$ \]
2. **Estimate the Cost of the 3001st Bagel**
To estimate the cost of producing the 3001st bagel, consider the incremental cost by examining the derivative if necessary and provide the answer to three decimal places.
\[ \text{Cost of the 3001st bagel} = \$ \]
#### Steps to Solve
1. **Substitute \( x = 3000 \) into the cost function**
\[ C(3000) = 300 + 0.25(3000) - 0.6 \left( \frac{3000}{1000} \right)^3 \]
2. **Simplify the Expression**
Calculate each term step-by-step to find the total cost.
3. **For the 3001st Bagel**
Approximate the marginal cost by differentiating \( C(x) \) and evaluating at \( x = 3000 \), or calculate \( C(3001) - C(3000) \).
#### Providing the Answers
Make sure to present your final answers clearly with the appropriate decimal precision as requested in the questions.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Similar questions
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)