Assume that the situation can be expressed as a linear cost function. Find the cost function. Fixed cost is $200, 50 items cost $1,700 to produce. The linear cost function is C(x)=
Assume that the situation can be expressed as a linear cost function. Find the cost function. Fixed cost is $200, 50 items cost $1,700 to produce. The linear cost function is C(x)=
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
3
Show work and no
Cursive writing
All parts
Get it right for a thumbs up
![### Understanding Linear Cost Functions
#### Problem Statement:
Assume that the situation can be expressed as a linear cost function. Find the cost function.
**Given Data:**
- Fixed cost is $200.
- The cost to produce 50 items is $1,700.
#### Finding the Linear Cost Function:
A linear cost function can be expressed in the form:
\[ C(x) = mx + b \]
where:
- \( C(x) \) is the total cost,
- \( m \) is the variable cost per unit,
- \( x \) is the number of units produced,
- \( b \) is the fixed cost.
**Step-by-Step Solution:**
1. **Identify the fixed cost \( b \):**
It is given that the fixed cost is $200.
Thus, \( b = 200 \).
2. **Set up the equation for the total cost of producing 50 items:**
Given that producing 50 items costs $1,700, we can set up the equation:
\[ C(50) = 50m + 200 = 1700 \]
3. **Solve for \( m \):**
\[ 50m + 200 = 1700 \]
Subtract 200 from both sides:
\[ 50m = 1500 \]
Divide by 50:
\[ m = 30 \]
**Conclusion:**
The linear cost function is:
\[ C(x) = 30x + 200 \]
This means the variable cost per unit is $30, and the fixed cost is $200.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97184fab-fce4-43b1-85fd-c47064c00bbe%2Fd46fa5cf-8ccf-4e53-be90-53538646290d%2Fmdpjrvq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Linear Cost Functions
#### Problem Statement:
Assume that the situation can be expressed as a linear cost function. Find the cost function.
**Given Data:**
- Fixed cost is $200.
- The cost to produce 50 items is $1,700.
#### Finding the Linear Cost Function:
A linear cost function can be expressed in the form:
\[ C(x) = mx + b \]
where:
- \( C(x) \) is the total cost,
- \( m \) is the variable cost per unit,
- \( x \) is the number of units produced,
- \( b \) is the fixed cost.
**Step-by-Step Solution:**
1. **Identify the fixed cost \( b \):**
It is given that the fixed cost is $200.
Thus, \( b = 200 \).
2. **Set up the equation for the total cost of producing 50 items:**
Given that producing 50 items costs $1,700, we can set up the equation:
\[ C(50) = 50m + 200 = 1700 \]
3. **Solve for \( m \):**
\[ 50m + 200 = 1700 \]
Subtract 200 from both sides:
\[ 50m = 1500 \]
Divide by 50:
\[ m = 30 \]
**Conclusion:**
The linear cost function is:
\[ C(x) = 30x + 200 \]
This means the variable cost per unit is $30, and the fixed cost is $200.
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