Suppose the Sunglasses Hut Company has a profit function given by P(q) = -0.01q² +5q — 42, where q is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in thousands of dollars, from selling and producing a pairs of sunglasses. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) Answer: MP(q) B) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.) = Answer: pairs of sunglasses need to be sold. thousand C) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.) thousand Answer: dollars of maximum profits can be expected.
Suppose the Sunglasses Hut Company has a profit function given by P(q) = -0.01q² +5q — 42, where q is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in thousands of dollars, from selling and producing a pairs of sunglasses. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) Answer: MP(q) B) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.) = Answer: pairs of sunglasses need to be sold. thousand C) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.) thousand Answer: dollars of maximum profits can be expected.
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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![**Profit Analysis for Sunglasses Hut Company**
Suppose the Sunglasses Hut Company has a profit function given by \( P(q) = -0.01q^2 + 5q - 42 \), where \( q \) is the number of thousands of pairs of sunglasses sold and produced, and \( P(q) \) is the total profit, in thousands of dollars, from selling and producing \( q \) pairs of sunglasses.
---
### A) Marginal Profit Function
**Task**: Find a simplified expression for the marginal profit function.
- **Answer**: \( MP(q) = \) [Provide your answer here]
---
### B) Maximizing Profit
**Task**: How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.)
- **Answer**: [Provide your answer here] thousand pairs of sunglasses need to be sold.
---
### C) Maximum Profit
**Task**: What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.)
- **Answer**: [Provide your answer here] thousand dollars of maximum profits can be expected.
---
By determining these values and understanding the profit function, the company can make informed decisions to optimize revenue and business strategy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24b715e5-d8b6-43f9-9aab-3a475648bab7%2Fc58d43e8-2b0b-4103-b8fd-e2a30fbeefa6%2F637fwae_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Profit Analysis for Sunglasses Hut Company**
Suppose the Sunglasses Hut Company has a profit function given by \( P(q) = -0.01q^2 + 5q - 42 \), where \( q \) is the number of thousands of pairs of sunglasses sold and produced, and \( P(q) \) is the total profit, in thousands of dollars, from selling and producing \( q \) pairs of sunglasses.
---
### A) Marginal Profit Function
**Task**: Find a simplified expression for the marginal profit function.
- **Answer**: \( MP(q) = \) [Provide your answer here]
---
### B) Maximizing Profit
**Task**: How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.)
- **Answer**: [Provide your answer here] thousand pairs of sunglasses need to be sold.
---
### C) Maximum Profit
**Task**: What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.)
- **Answer**: [Provide your answer here] thousand dollars of maximum profits can be expected.
---
By determining these values and understanding the profit function, the company can make informed decisions to optimize revenue and business strategy.
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