An ice cream shop finds that its weekly profit P (in dollars) as a function of the price a (in dollars) it charges per ice cream cone is given by the function g, defined by g(x) = – 110z? + 700x – 120. a. What price should the store charge to maximize their profit? Need a hint? $ 35/11 Preview b. According to the model, what is the store's maximum weekly profit? Need a hint? $ 10930/11 Preview c. What prices would cause the weekly profit to be $0? (Write your answers as a comma-separated list.) Need a hint? $ 6.18,0.18 Preview
An ice cream shop finds that its weekly profit P (in dollars) as a function of the price a (in dollars) it charges per ice cream cone is given by the function g, defined by g(x) = – 110z? + 700x – 120. a. What price should the store charge to maximize their profit? Need a hint? $ 35/11 Preview b. According to the model, what is the store's maximum weekly profit? Need a hint? $ 10930/11 Preview c. What prices would cause the weekly profit to be $0? (Write your answers as a comma-separated list.) Need a hint? $ 6.18,0.18 Preview
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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![### Ice Cream Shop Profit Model
An ice cream shop finds that its weekly profit \( P \) (in dollars) as a function of the price \( x \) (in dollars) it charges per ice cream cone is given by the function \( g \), defined by:
\[ g(x) = -110x^2 + 700x - 120 \]
**a. Maximizing Profit**
- **Question:** What price should the store charge to maximize their profit?
- **Answer:** \( \frac{35}{11} \)
**b. Maximum Weekly Profit**
- **Question:** According to the model, what is the store's maximum weekly profit?
- **Answer:** \( \frac{10930}{11} \)
**c. Prices for Zero Profit**
- **Question:** What prices would cause the weekly profit to be $0? (Write your answers as a comma-separated list.)
- **Answer:** \( 6, 18, 0.18 \)
**d. Comparison with Another Store's Model**
Another ice cream shop developed a similar model for their weekly profit. Its model is \( f \) where:
\[ f(x) = g(x) + 475 \]
**Implications:**
- ✔️ When this shop charges the same price per ice cream cone, it will always earn an additional $475 per week compared to the original store.
- ❌ When this shop charges the same price per ice cream cone, it will always earn $475 per week less than the original store.
- ✔️ The two stores have different maximum weekly profits.
- ✔️ To maximize weekly profits, both stores should charge the same price per cone.
This exercise illustrates how changing the pricing model impacts the profitability of a business.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2810685e-1eeb-461a-9149-0ef27d84930f%2Fa57ac872-2c03-48b7-b8fd-183c90cbcf75%2F1j3e2rm_processed.png&w=3840&q=75)
Transcribed Image Text:### Ice Cream Shop Profit Model
An ice cream shop finds that its weekly profit \( P \) (in dollars) as a function of the price \( x \) (in dollars) it charges per ice cream cone is given by the function \( g \), defined by:
\[ g(x) = -110x^2 + 700x - 120 \]
**a. Maximizing Profit**
- **Question:** What price should the store charge to maximize their profit?
- **Answer:** \( \frac{35}{11} \)
**b. Maximum Weekly Profit**
- **Question:** According to the model, what is the store's maximum weekly profit?
- **Answer:** \( \frac{10930}{11} \)
**c. Prices for Zero Profit**
- **Question:** What prices would cause the weekly profit to be $0? (Write your answers as a comma-separated list.)
- **Answer:** \( 6, 18, 0.18 \)
**d. Comparison with Another Store's Model**
Another ice cream shop developed a similar model for their weekly profit. Its model is \( f \) where:
\[ f(x) = g(x) + 475 \]
**Implications:**
- ✔️ When this shop charges the same price per ice cream cone, it will always earn an additional $475 per week compared to the original store.
- ❌ When this shop charges the same price per ice cream cone, it will always earn $475 per week less than the original store.
- ✔️ The two stores have different maximum weekly profits.
- ✔️ To maximize weekly profits, both stores should charge the same price per cone.
This exercise illustrates how changing the pricing model impacts the profitability of a business.
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