Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
For a certain company, the cost function for producing z items is C (z) = 30 z + 150 and the revenue function for selling z items is R (x) = –0.5(x – 70)² + 2,450. The maximum capacity of the company is 100 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C (1) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! Answers to some of the questions are given below so that you can check your work. 1. Assuming that the company sells all that it produces, what is the profit function? P(z) =| 国团。 Hint: Profit = Revenue - Cost as we examined in Discussion 3. 2. What is the domain of P (x)? Hint: Does calculating P (z) make sense when æ = -10 or z = 1,000? 3. The company can choose to produce either 40 or 50 items. What is their profit for each case, and which level of production should they choose? Profit when producing 40 items = Number Profit when producing 50 items = Number 4. Can you explain, from our model, why the company makes less profit when producing 10 more units?

For a certain company, the cost function for producing z items is C (z) = 30 z + 150 and the revenue function for selling z items is R (x) = –0.5(x – 70)² + 2,450. The maximum capacity of the company is 100 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C (1) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! Answers to some of the questions are given below so that you can check your work. 1. Assuming that the company sells all that it produces, what is the profit function? P(z) =| 国团。 Hint: Profit = Revenue - Cost as we examined in Discussion 3. 2. What is the domain of P (x)? Hint: Does calculating P (z) make sense when æ = -10 or z = 1,000? 3. The company can choose to produce either 40 or 50 items. What is their profit for each case, and which level of production should they choose? Profit when producing 40 items = Number Profit when producing 50 items = Number 4. Can you explain, from our model, why the company makes less profit when producing 10 more units?

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.1: Quadratic Functions
Problem 6SC: A company that makes and sells baseball caps has found that the total monthly cost C in dollars of...
See similar textbooks
icon
Related questions
Question
For a certain company, the cost function for producing a items is C (x) = 30 z + 150 and the revenue function for selling a items is R(x) = -0.5(x – 70)2 + 2,450. The maximum capacity of the company is 100 items. The profit function P(æ) is the revenue function R(r) (how much it takes in) minus the cost function C (r) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! Answers to some of the questions are given below so that you can check your work. 1. Assuming that the company sells all that it produces, what is the profit function? P(z) =| Hint: Profit = Revenue - Cost as we examined in Discussion 3. 2. What is the domain of P (x)? Hint: Does calculating P(x) make sense when a = -10 or x = 1,000? 3. The company can choose to produce either 40 or 50 items. What is their profit for each case, and which level of production should they choose? Profit when producing 40 items = Number Profit when producing 50 items = Number 4. Can you explain, from our model, why the company makes less profit when producing 10 more units?
Transcribed Image Text:For a certain company, the cost function for producing a items is C (x) = 30 z + 150 and the revenue function for selling a items is R(x) = -0.5(x – 70)2 + 2,450. The maximum capacity of the company is 100 items. The profit function P(æ) is the revenue function R(r) (how much it takes in) minus the cost function C (r) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! Answers to some of the questions are given below so that you can check your work. 1. Assuming that the company sells all that it produces, what is the profit function? P(z) =| Hint: Profit = Revenue - Cost as we examined in Discussion 3. 2. What is the domain of P (x)? Hint: Does calculating P(x) make sense when a = -10 or x = 1,000? 3. The company can choose to produce either 40 or 50 items. What is their profit for each case, and which level of production should they choose? Profit when producing 40 items = Number Profit when producing 50 items = Number 4. Can you explain, from our model, why the company makes less profit when producing 10 more units?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS