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Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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Question
![**Problem Statement:**
Determine the profit function for the given revenue and cost functions.
**Revenue Function:**
\[ R(x) = 140x \]
**Cost Function:**
\[ C(x) = 78.5x + 10,455 \]
**Profit Function:**
\[ P(x) = \boxed{} \]
Determine the break-even point.
**Break-Even Point:**
\[ x = \boxed{} \]
**Explanation:**
To find the profit function \( P(x) \), subtract the cost function \( C(x) \) from the revenue function \( R(x) \):
\[ P(x) = R(x) - C(x) \]
To determine the break-even point, solve for \( x \) when the profit function \( P(x) = 0 \). This is the point where total revenue equals total cost.](https://content.bartleby.com/qna-images/question/b0d79c4c-40ce-427b-b4a0-26ffd9f423cd/beb01360-34f1-4bf8-b347-0ad50ce06c2a/atxb23a_thumbnail.png)
Transcribed Image Text:**Problem Statement:**
Determine the profit function for the given revenue and cost functions.
**Revenue Function:**
\[ R(x) = 140x \]
**Cost Function:**
\[ C(x) = 78.5x + 10,455 \]
**Profit Function:**
\[ P(x) = \boxed{} \]
Determine the break-even point.
**Break-Even Point:**
\[ x = \boxed{} \]
**Explanation:**
To find the profit function \( P(x) \), subtract the cost function \( C(x) \) from the revenue function \( R(x) \):
\[ P(x) = R(x) - C(x) \]
To determine the break-even point, solve for \( x \) when the profit function \( P(x) = 0 \). This is the point where total revenue equals total cost.
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