A particular computing company finds that its weekly profit, in dollars, from the production and sale of x laptop computers is P(x) = -0.006x³-0.3x² +500x-700. Currently the company builds and sells 11 laptops weekly. a) What is the current weekly profit? b) How much profit would be lost if production and sales dropped to 10 laptops weekly? c) What is the marginal profit when x = 11? d) Use the answer from part (a) and (c) to estimate the profit resulting from the production and sale of 12 laptops weekly. a) The current weekly profit is $ (Round to the nearest cent as needed.) b) The decrease in profit is $ (Round to the nearest cent as needed) c) The marginal profit when x = 11 is $ (Round to the nearest cent as needed.) d) The profit resulting from the production and sale of 12 laptops weekly is approximately $ (Round to the nearest cent as needed.)
A particular computing company finds that its weekly profit, in dollars, from the production and sale of x laptop computers is P(x) = -0.006x³-0.3x² +500x-700. Currently the company builds and sells 11 laptops weekly. a) What is the current weekly profit? b) How much profit would be lost if production and sales dropped to 10 laptops weekly? c) What is the marginal profit when x = 11? d) Use the answer from part (a) and (c) to estimate the profit resulting from the production and sale of 12 laptops weekly. a) The current weekly profit is $ (Round to the nearest cent as needed.) b) The decrease in profit is $ (Round to the nearest cent as needed) c) The marginal profit when x = 11 is $ (Round to the nearest cent as needed.) d) The profit resulting from the production and sale of 12 laptops weekly is approximately $ (Round to the nearest cent as needed.)
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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![### Title: Calculating Weekly Profit from Laptop Sales
A particular computing company finds that its weekly profit, in dollars, from the production and sale of \( x \) laptop computers is given by the polynomial:
\[ P(x) = -0.006x^3 - 0.3x^2 + 500x - 700 \]
Currently, the company builds and sells 11 laptops weekly.
#### Questions:
a) **What is the current weekly profit?**
b) **How much profit would be lost if production and sales dropped to 10 laptops weekly?**
c) **What is the marginal profit when \( x = 11 \)?**
d) **Use the answer from part (a) and (c) to estimate the profit resulting from the production and sale of 12 laptops weekly.**
---
#### Solutions:
- **a)** The current weekly profit is $[ \_\_ ] (Round to the nearest cent as needed.)
- **b)** The decrease in profit is $[ \_\_ ] (Round to the nearest cent as needed.)
- **c)** The marginal profit when \( x = 11 \) is $[ \_\_ ] (Round to the nearest cent as needed.)
- **d)** The profit resulting from the production and sale of 12 laptops weekly is approximately $[ \_\_ ] (Round to the nearest cent as needed.)
---
The polynomial \( P(x) \) helps the company to determine optimal production levels and understand the implications of changing production quantities. The marginal profit is particularly useful for assessing the profitability of producing an additional unit. Remember to round all final answers to the nearest cent for precision.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b683749-58e5-4e30-bd6b-95e0226f4526%2F6970f0ff-5c20-4eeb-840e-29b06302ba7c%2Fhhjk1cp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Title: Calculating Weekly Profit from Laptop Sales
A particular computing company finds that its weekly profit, in dollars, from the production and sale of \( x \) laptop computers is given by the polynomial:
\[ P(x) = -0.006x^3 - 0.3x^2 + 500x - 700 \]
Currently, the company builds and sells 11 laptops weekly.
#### Questions:
a) **What is the current weekly profit?**
b) **How much profit would be lost if production and sales dropped to 10 laptops weekly?**
c) **What is the marginal profit when \( x = 11 \)?**
d) **Use the answer from part (a) and (c) to estimate the profit resulting from the production and sale of 12 laptops weekly.**
---
#### Solutions:
- **a)** The current weekly profit is $[ \_\_ ] (Round to the nearest cent as needed.)
- **b)** The decrease in profit is $[ \_\_ ] (Round to the nearest cent as needed.)
- **c)** The marginal profit when \( x = 11 \) is $[ \_\_ ] (Round to the nearest cent as needed.)
- **d)** The profit resulting from the production and sale of 12 laptops weekly is approximately $[ \_\_ ] (Round to the nearest cent as needed.)
---
The polynomial \( P(x) \) helps the company to determine optimal production levels and understand the implications of changing production quantities. The marginal profit is particularly useful for assessing the profitability of producing an additional unit. Remember to round all final answers to the nearest cent for precision.
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