A food truck's profit from the sale of b beef burgers and v veggie burgers can be described by the function P(b,v) dollars. The following values are given: P(50,30)=240; Po(50,30)= 2.6; P,(50,30)-3.6 (a) Estimate the food truck's profit if they continue to sell 30 veggie burgers, but are only able to sell 45 beef burgers. (Round to the nearest cent.) $ (b)If the food truck is only able to sell 45 beef burgers, but wants maintain their profit of $240, how many veggie burgers would they need to sell to compensate for the decrease in beef burgers? (Round decimal values up to the next whole number.) veggie burgers
A food truck's profit from the sale of b beef burgers and v veggie burgers can be described by the function P(b,v) dollars. The following values are given: P(50,30)=240; Po(50,30)= 2.6; P,(50,30)-3.6 (a) Estimate the food truck's profit if they continue to sell 30 veggie burgers, but are only able to sell 45 beef burgers. (Round to the nearest cent.) $ (b)If the food truck is only able to sell 45 beef burgers, but wants maintain their profit of $240, how many veggie burgers would they need to sell to compensate for the decrease in beef burgers? (Round decimal values up to the next whole number.) veggie burgers
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![---
### Problem Description
A food truck's profit from the sale of \( b \) beef burgers and \( v \) veggie burgers can be described by the function \( P(b,v) \) dollars.
### Given Data
The following values are provided:
- \( P(50,30) = 240 \)
- \( P_b(50,30) = 2.6 \)
- \( P_v(50,30) = 3.6 \)
### Questions
1. **Part (a)**
**Estimate the food truck's profit if they continue to sell 30 veggie burgers, but are only able to sell 45 beef burgers. (Round to the nearest cent.)**
\[
\text{Profit: } \$ \boxed{}
\]
2. **Part (b)**
**If the food truck is only able to sell 45 beef burgers, but wants to maintain their profit of $240, how many veggie burgers would they need to sell to compensate for the decrease in beef burgers? (Round decimal values up to the next whole number.)**
\[
\text{Number of veggie burgers: } \boxed{}
\]
### Explanation of Given Data
1. \( P(50,30) \): The profit when 50 beef burgers and 30 veggie burgers are sold is $240.
2. \( P_b(50,30) \): The partial derivative of the profit function with respect to beef burgers at the point (50 beef and 30 veggie burgers) is 2.6. This signifies that for every additional beef burger sold, the profit increases by $2.6.
3. \( P_v(50,30) \): The partial derivative of the profit function with respect to veggie burgers at the point (50 beef and 30 veggie burgers) is 3.6. This indicates that for every additional veggie burger sold, the profit increases by $3.6.
Please solve the questions as directed, ensuring to round the final answers appropriately as per the instructions.
---
When presenting this on an educational website, ensure to clearly separate the problem statement, the provided values, and the questions. Detailed explanations can aid in better understanding and contextual learning for students.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcfa3f98-eb44-4f4d-86d7-8c297108b84f%2Ffdc0dd5c-3b16-450f-9ba4-bf27850c4efd%2Frvg21bm_processed.png&w=3840&q=75)
Transcribed Image Text:---
### Problem Description
A food truck's profit from the sale of \( b \) beef burgers and \( v \) veggie burgers can be described by the function \( P(b,v) \) dollars.
### Given Data
The following values are provided:
- \( P(50,30) = 240 \)
- \( P_b(50,30) = 2.6 \)
- \( P_v(50,30) = 3.6 \)
### Questions
1. **Part (a)**
**Estimate the food truck's profit if they continue to sell 30 veggie burgers, but are only able to sell 45 beef burgers. (Round to the nearest cent.)**
\[
\text{Profit: } \$ \boxed{}
\]
2. **Part (b)**
**If the food truck is only able to sell 45 beef burgers, but wants to maintain their profit of $240, how many veggie burgers would they need to sell to compensate for the decrease in beef burgers? (Round decimal values up to the next whole number.)**
\[
\text{Number of veggie burgers: } \boxed{}
\]
### Explanation of Given Data
1. \( P(50,30) \): The profit when 50 beef burgers and 30 veggie burgers are sold is $240.
2. \( P_b(50,30) \): The partial derivative of the profit function with respect to beef burgers at the point (50 beef and 30 veggie burgers) is 2.6. This signifies that for every additional beef burger sold, the profit increases by $2.6.
3. \( P_v(50,30) \): The partial derivative of the profit function with respect to veggie burgers at the point (50 beef and 30 veggie burgers) is 3.6. This indicates that for every additional veggie burger sold, the profit increases by $3.6.
Please solve the questions as directed, ensuring to round the final answers appropriately as per the instructions.
---
When presenting this on an educational website, ensure to clearly separate the problem statement, the provided values, and the questions. Detailed explanations can aid in better understanding and contextual learning for students.
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