A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $6, and the society sells an average of 24 feeders per week at a price of $10 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses two sales per week. (a) Find a function P that models weekly profit in terms of price per feeder. (Let x represent the number of dollars the price is increased.) P(x) = (b) What ticket price is so high that no profit is generated? $ (c) The society needs to make a weekly profit of $110 to cover the expenses of their nature center. What price should the society charge per feeder to meet this goal? $ (smaller value) (larger value) $
A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $6, and the society sells an average of 24 feeders per week at a price of $10 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses two sales per week. (a) Find a function P that models weekly profit in terms of price per feeder. (Let x represent the number of dollars the price is increased.) P(x) = (b) What ticket price is so high that no profit is generated? $ (c) The society needs to make a weekly profit of $110 to cover the expenses of their nature center. What price should the society charge per feeder to meet this goal? $ (smaller value) (larger value) $
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
I tried to do it and couldn’t figure it out can you please do step by step thank you !
![**A Community Bird-Watching Society's Pricing Model**
The community bird-watching society aims to fund its conservation activities by making and selling simple bird feeders. Below is a breakdown of their pricing and profit strategy:
**Current Sales Information**
- **Cost of materials per feeder:** $6
- **Current selling price per feeder:** $10
- **Average sales per week:** 24 feeders
**Survey Findings**
The society conducted a survey and discovered that for every $1 increase in the price of a feeder, they experience a loss of two sales per week.
**Problems to Solve:**
**(a) Develop a profit function**
Create a function \( P \) that models weekly profit in terms of price per feeder. Let \( x \) represent the number of dollars the price is increased.
- **Profit function \( P(x) = \):** [Blank space for function]
**(b) Determine when no profit is made**
Identify the ticket price at which no profit is generated.
- **No profit ticket price: $** [Blank space for price]
**(c) Meet specific profit requirement**
The society needs to generate a weekly profit of $110 to cover the expenses of their nature center.
- **Smaller price option per feeder: $** [Blank space for price]
- **Larger price option per feeder: $** [Blank space for price]
In this task, you will apply algebraic methods to derive the function for \( P(x) \), solve for the conditions under which profit is zero, and determine the ticket prices that help achieve the specific profit goal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb96cbef8-ab64-43b1-a923-6a8582f58768%2F50cd882f-91b5-4f5a-84c9-0754afe85ff1%2F56l8l3p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**A Community Bird-Watching Society's Pricing Model**
The community bird-watching society aims to fund its conservation activities by making and selling simple bird feeders. Below is a breakdown of their pricing and profit strategy:
**Current Sales Information**
- **Cost of materials per feeder:** $6
- **Current selling price per feeder:** $10
- **Average sales per week:** 24 feeders
**Survey Findings**
The society conducted a survey and discovered that for every $1 increase in the price of a feeder, they experience a loss of two sales per week.
**Problems to Solve:**
**(a) Develop a profit function**
Create a function \( P \) that models weekly profit in terms of price per feeder. Let \( x \) represent the number of dollars the price is increased.
- **Profit function \( P(x) = \):** [Blank space for function]
**(b) Determine when no profit is made**
Identify the ticket price at which no profit is generated.
- **No profit ticket price: $** [Blank space for price]
**(c) Meet specific profit requirement**
The society needs to generate a weekly profit of $110 to cover the expenses of their nature center.
- **Smaller price option per feeder: $** [Blank space for price]
- **Larger price option per feeder: $** [Blank space for price]
In this task, you will apply algebraic methods to derive the function for \( P(x) \), solve for the conditions under which profit is zero, and determine the ticket prices that help achieve the specific profit goal.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education