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 Statement**
A company determines the price \( p \) to sell \( x \) Fans is:
\[ \text{Revenue} = 280x - 0.4x^2 \]
The cost to produce \( x \) Fans is:
\[ C = 5000 + 0.6x^2 \]
**Question**
How many Fans must the company sell to maximize profit?
---
**Note**
To solve this problem, set up the profit function \( P(x) \) as the revenue function minus the cost function:
\[ P(x) = (280x - 0.4x^2) - (5000 + 0.6x^2) \]
Simplify and find the derivative \( P'(x) \) to locate the maximum profit by setting \( P'(x) = 0 \). Solve for \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc17f3f0c-3f3b-4d84-90ac-d23f7cabcc9b%2F95565bca-fa33-4732-b2bc-364552294138%2Favhme5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement**
A company determines the price \( p \) to sell \( x \) Fans is:
\[ \text{Revenue} = 280x - 0.4x^2 \]
The cost to produce \( x \) Fans is:
\[ C = 5000 + 0.6x^2 \]
**Question**
How many Fans must the company sell to maximize profit?
---
**Note**
To solve this problem, set up the profit function \( P(x) \) as the revenue function minus the cost function:
\[ P(x) = (280x - 0.4x^2) - (5000 + 0.6x^2) \]
Simplify and find the derivative \( P'(x) \) to locate the maximum profit by setting \( P'(x) = 0 \). Solve for \( x \).
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