### Calculating Production Costs for Bagels#### Cost FunctionThe 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 Solve1. **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 Solve1. **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 AnswersMake sure to present your final answers clearly with the appropriate decimal precision as requested in the questions.

Answered: Image /qna-images/answer/20167401-d532-40b0-9a92-e137701e5d53.jpg

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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.

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