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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Question

### 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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