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
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![### 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.
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