Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

At the surface of the ocean, the water pressure i…

02:34

Question

Answered step-by-step

Problem 18 Medium Difficulty

The manager of a furniture factory finds that it costs\ $2200 to manufacture 100 chairs in one day and \$4800 to produce 300 chairs in one day.
(a) Express the cost as a function of the number of chairs produced, assuming that it is linear. Then sketch the graph.
(b) What is the slope of the graph and what does it represent?
(c) What is the y-intercept of the graph and what does it represent?


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Heather Zimmers
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Heather Zimmers

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

02:36

Jeffrey Payo

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 2

Mathematical Models: A Catalog of Essential Functions

Related Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Discussion

You must be signed in to discuss.
Top Calculus 3 Educators
Lily An

Johns Hopkins University

Anna Marie Vagnozzi

Campbell University

Caleb Elmore

Baylor University

Samuel Hannah

University of Nottingham

Calculus 3 Courses

Lectures

Video Thumbnail

04:31

Multivariate Functions - Intro

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

Video Thumbnail

12:15

Partial Derivatives - Overview

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

Join Course
Recommended Videos

0:00

The manager of a furniture…

08:41

The manager of a furniture…

06:22

The manager of a furniture…

03:57

The manager of a furniture…

09:33

The manager of a furniture…

03:20

The manager of a furniture…

04:03

Manufacturing cost The man…

02:59

Manufacturing cost The man…

03:21

A plant can manufacture 80…

0:00

The daily cost to the manu…

Watch More Solved Questions in Chapter 1

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32

Video Transcript

all right. This problem gives us a situation where there's a furniture factory and they're manufacturing chairs, and we want to express the cost as a function of the number of chairs produced, so cost will be our Y. Coordinate and number of chairs are X. I'm going to use end to stand for the number of chairs and see to stand for the cost. And they give us some data in the problem that we can translate into ordered pairs. For 100 chairs manufactured in a day, it costs $2200 and for 300 shares manufactured in a day, it costs $4800. So let's use those two points and find the equation of the line. And this is part A. So we can start by finding the slope changing. Why 4800 minus 2200 over Change in x 300 minus 100 gives us 2600 divided by 200 that's 13 and then we can use our point slope form. Why minus y one equals M times X minus X one. We can use one of our two points. It doesn't matter which, so I'll just use the 1st 1 Why minus 2200 equals 13 times X minus 100 and we can simplify that. First will distribute the 13. So why minus 2200 equals 13 x minus 1300 and then we'll add 2200 to both sides. So why equals 13 X plus 900? Now if I want to put it into the variables that I chose instead of X and Y will say that, see, the cost equals 13 times and the number of chairs plus 900. So there's our linear model, and now we can make a sketch of it. So let's assume that they're not going to make a negative number of chairs. So we'll just focus on quadrant one number of chairs on X cost on Why go buy one hundreds on the X axis and I'll go buy one thousands on the Y axis. Now, remember, we just found our equation that has a Y intercept of 900 so we can pull at that point and we have the 0.122 100 and we have the 0.348 100 and those should fall in a line. And so there's a sketch of the graph. All right, The next thing we want to look at is what is the slope and what does it represent? So if we look back at the function we found the slope was 13. And if you think about the units the units on, why was ah, the cost? So that would be dollars and the units on X, that was the number of chairs, so dollars per chair. So it's $13 more for every chair increased cost $13 per chair. Okay, how about the Y intercept? We can see from our equation that the Y intercept is 900. That would correspond to the 0.0 comma. 900 and zero would be the number of chairs made. So if they make zero chairs, they still have a cost of $900 per day at their manufacturing plant.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
192
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
82
Hosted by: Alonso M
See More

Related Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Top Calculus 3 Educators
Lily An

Johns Hopkins University

Anna Marie Vagnozzi

Campbell University

Caleb Elmore

Baylor University

Samuel Hannah

University of Nottingham

Calculus 3 Courses

Lectures

Video Thumbnail

04:31

Multivariate Functions - Intro

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

Video Thumbnail

12:15

Partial Derivatives - Overview

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

Join Course
Recommended Videos

0:00

The manager of a furniture factory finds that it costs\ $2200 to manufacture 10…

08:41

The manager of a furniture factory finds that it costs $\$ 2200$ to manufacture…

06:22

The manager of a furniture factory finds that it costs $2200 to manufacture 100…

03:57

The manager of a furniture factory finds that it costs $\$ 2200$ to manufactur…

09:33

The manager of a furniture factory finds that it costs $\$ 2200$ to manufactur…

03:20

The manager of a furniture factory finds that it costs $\$ 2200$ to produce 100…

04:03

Manufacturing cost The manager of a furniture factory finds that it costs 2200 …

02:59

Manufacturing cost The manager of a furniture factory finds that it costs $\$ …

03:21

A plant can manufacture 80 golf clubs per day for a total daily cost of $\$ 7,6…

0:00

The daily cost to the manufacturing company is modeled by the function $C(x)=7.…
Additional Mathematics Questions

02:03

'pakisagot po pls kailangan ko na po ngayon arawNONSENSE =REPORT
Ka…

02:45

'ayan na pasagot brainliest kita
Learning Task 1. Complete the table…

02:39

"please help me answer this thank you
A fish ball stall can earned …

02:44

"Complete the table below by determining the values (a) f(-3), (b) f(1)…

01:04

'42. The following raw data are the scores of the students in Grade 7 -…

02:43

'Learning task 4: Do the following in your notebook. (A.) Find the equa…

02:13

'kailangan na po bukas pasagot naman ng maayos
\
nonsense answer=…

05:04

4. Use the method of cylindrical shells to find the volume V generated by ro…

01:43

Use slope to determine if lines PQ and RS are Parallel. Perpendicular, or ne…

03:51

Give an example of a function nf of three variables with an absolute maximum…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started