Payton is making stuffed animal keychains out of yarn. She set up an Etsy page to sell her keychain and that cost her $32 to set up. Each keychain she makes requires a $1.50 amount of yarn. She decides to sell each keychain for $8. What is total cost function that Payton will need to pay for?
Payton is making stuffed animal keychains out of yarn. She set up an Etsy page to sell her keychain and that cost her $32 to set up. Each keychain she makes requires a $1.50 amount of yarn. She decides to sell each keychain for $8. What is total cost function that Payton will need to pay for?
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...
Related questions
Question
![**Problem Statement:**
Payton is making stuffed animal keychains out of yarn. She set up an Etsy page to sell her keychains, and that cost her $32 to set up. Each keychain she makes requires $1.50 worth of yarn. She decides to sell each keychain for $8.
**Question:**
What is the total cost function that Payton will need to pay for?
**Explanation:**
To calculate the total cost function that Payton will need to pay for, we need to factor in both the fixed cost and the variable cost:
1. **Fixed Cost:** This is the one-time setup fee for the Etsy page, which is $32.
2. **Variable Cost:** This is the cost of materials (yarn) for each keychain. Payton requires $1.50 worth of yarn per keychain.
**Total Cost** (C) can be expressed as a function of the number of keychains (x) Payton makes.
\[ C(x) = \text{Fixed Cost} + (\text{Variable Cost per Keychain} \times \text{Number of Keychains}) \]
Given the fixed cost is $32 and the variable cost per keychain is $1.50, the cost function becomes:
\[ C(x) = 32 + 1.50x \]
This function will help Payton determine her total costs based on the number of keychains she decides to make.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09b3997c-2096-4573-b74b-055c69181c0d%2F90ef511c-c11f-41fe-ba6f-c7ccfe8a1218%2F5qk712f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Payton is making stuffed animal keychains out of yarn. She set up an Etsy page to sell her keychains, and that cost her $32 to set up. Each keychain she makes requires $1.50 worth of yarn. She decides to sell each keychain for $8.
**Question:**
What is the total cost function that Payton will need to pay for?
**Explanation:**
To calculate the total cost function that Payton will need to pay for, we need to factor in both the fixed cost and the variable cost:
1. **Fixed Cost:** This is the one-time setup fee for the Etsy page, which is $32.
2. **Variable Cost:** This is the cost of materials (yarn) for each keychain. Payton requires $1.50 worth of yarn per keychain.
**Total Cost** (C) can be expressed as a function of the number of keychains (x) Payton makes.
\[ C(x) = \text{Fixed Cost} + (\text{Variable Cost per Keychain} \times \text{Number of Keychains}) \]
Given the fixed cost is $32 and the variable cost per keychain is $1.50, the cost function becomes:
\[ C(x) = 32 + 1.50x \]
This function will help Payton determine her total costs based on the number of keychains she decides to make.
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 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning