The Student Government Association is making Mother's Day gift baskets to sell at a fund-raiser. If the SGA makes a larger quantity of baskets, 6x +1 x+60 it can purchase materials in bulk. The total cost (in hundreds of dollars) of making x gift baskets can be approximated by C(x)=- Complete parts (a) through (c) below. The marginal cost function is The marginal cost at x = 10 is $/basket. (Round to the nearest cent as needed) The marginal cost at x = 20 is $/basket. (Round to the nearest cent as needed.) (b) Find the average-cost function and the average cost at x = 10 and x = 20. The average-cost function is. The average cost at x = 10 is $/basket. (Round to the nearest cent as needed.) The average cost at x = 20 is $/basket.
The Student Government Association is making Mother's Day gift baskets to sell at a fund-raiser. If the SGA makes a larger quantity of baskets, 6x +1 x+60 it can purchase materials in bulk. The total cost (in hundreds of dollars) of making x gift baskets can be approximated by C(x)=- Complete parts (a) through (c) below. The marginal cost function is The marginal cost at x = 10 is $/basket. (Round to the nearest cent as needed) The marginal cost at x = 20 is $/basket. (Round to the nearest cent as needed.) (b) Find the average-cost function and the average cost at x = 10 and x = 20. The average-cost function is. The average cost at x = 10 is $/basket. (Round to the nearest cent as needed.) The average cost at x = 20 is $/basket.
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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![The Student Government Association (SGA) is making Mother's Day gift baskets to sell at a fundraiser. If the SGA produces a larger quantity of baskets, it can purchase materials in bulk. The total cost \( C(x) \), in hundreds of dollars, of making \( x \) gift baskets can be approximated by the function:
\[ C(x) = \frac{6x + 1}{x + 60} \]
Complete parts (a) through (c) below.
---
### (a) Marginal Cost Function
1. **The marginal cost function is [ ].**
2. **The marginal cost at \( x = 10 \) is $[ ]/basket.**
- *(Round to the nearest cent as needed.)*
3. **The marginal cost at \( x = 20 \) is $[ ]/basket.**
- *(Round to the nearest cent as needed.)*
### (b) Average-Cost Function
1. **The average-cost function is [ ].**
2. **The average cost at \( x = 10 \) is $[ ]/basket.**
- *(Round to the nearest cent as needed.)*
3. **The average cost at \( x = 20 \) is $[ ]/basket.**
- *(Round to the nearest cent as needed.)*
### Explanation of Terms:
- **Marginal Cost Function:** This represents the additional cost of producing one more gift basket. It is derived by taking the derivative of the total cost function \( C(x) \).
- **Average-Cost Function:** This is the total cost divided by the number of baskets, showing the cost per basket.
These calculations help in understanding the cost behavior as production scales, allowing more informed decision-making about quantities to produce and sell.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3f191a8-a1b2-42ed-ac9e-32d60645d728%2Fece662f4-18a7-4c3e-82c9-00bf5c9568ad%2Fbh58itg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The Student Government Association (SGA) is making Mother's Day gift baskets to sell at a fundraiser. If the SGA produces a larger quantity of baskets, it can purchase materials in bulk. The total cost \( C(x) \), in hundreds of dollars, of making \( x \) gift baskets can be approximated by the function:
\[ C(x) = \frac{6x + 1}{x + 60} \]
Complete parts (a) through (c) below.
---
### (a) Marginal Cost Function
1. **The marginal cost function is [ ].**
2. **The marginal cost at \( x = 10 \) is $[ ]/basket.**
- *(Round to the nearest cent as needed.)*
3. **The marginal cost at \( x = 20 \) is $[ ]/basket.**
- *(Round to the nearest cent as needed.)*
### (b) Average-Cost Function
1. **The average-cost function is [ ].**
2. **The average cost at \( x = 10 \) is $[ ]/basket.**
- *(Round to the nearest cent as needed.)*
3. **The average cost at \( x = 20 \) is $[ ]/basket.**
- *(Round to the nearest cent as needed.)*
### Explanation of Terms:
- **Marginal Cost Function:** This represents the additional cost of producing one more gift basket. It is derived by taking the derivative of the total cost function \( C(x) \).
- **Average-Cost Function:** This is the total cost divided by the number of baskets, showing the cost per basket.
These calculations help in understanding the cost behavior as production scales, allowing more informed decision-making about quantities to produce and sell.
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