2. A company has determined that the demand function for a certain couch is given by p = 4000 - 0.25x, where p is the price per couch and x is the number of couches sold. The fixed costs associated with producing a line of couches is $500,000, and each couch costs $280 to make. a. Start by finding functions to represent the revenue b. and the total cost c. then find a function for profit d. Determine how many couches should be manufactured and sold in order to maximize profit. Show Work and Write a Sentence!
2. A company has determined that the demand function for a certain couch is given by p = 4000 - 0.25x, where p is the price per couch and x is the number of couches sold. The fixed costs associated with producing a line of couches is $500,000, and each couch costs $280 to make. a. Start by finding functions to represent the revenue b. and the total cost c. then find a function for profit d. Determine how many couches should be manufactured and sold in order to maximize profit. Show Work and Write a Sentence!
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,...
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![### Problem Statement
A company has determined that the demand function for a certain couch is given by
\[ p = 4000 - 0.25x \]
where \( p \) is the price per couch, and \( x \) is the number of couches sold. The fixed costs associated with producing a line of couches is $500,000, and each couch costs $280 to make.
**a.** Start by finding functions to represent the revenue.
**b.** Calculate the total cost.
**c.** Then find a function for profit.
**d.** Determine how many couches should be manufactured and sold in order to maximize profit.
**Show Work and Write a Sentence!**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04d5ed65-3ad4-46a9-9e82-b3fe58bfd913%2Ffeb50d0d-396c-452d-97a0-22ab512c44d4%2Flej9bsl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A company has determined that the demand function for a certain couch is given by
\[ p = 4000 - 0.25x \]
where \( p \) is the price per couch, and \( x \) is the number of couches sold. The fixed costs associated with producing a line of couches is $500,000, and each couch costs $280 to make.
**a.** Start by finding functions to represent the revenue.
**b.** Calculate the total cost.
**c.** Then find a function for profit.
**d.** Determine how many couches should be manufactured and sold in order to maximize profit.
**Show Work and Write a Sentence!**
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