For a certain company, the cost function for producing x items is C(x)=40x+100 and the revenue function for selling x items is R(x)=−0.5(x−100)2+5,000. The maximum capacity of the company is 150 items. The profit function P(x) is the revenue function R(x) (how much it takes in)  minus the cost function C(x) (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. Assuming that the company sells all that it produces, what is the profit function? P(x)=   . Hint: Profit = Revenue - Cost as we examined in Discussion 3. What is the domain of P(x)? Hint: Does calculating P(x) make sense when x=−10 or x=1,000? The company can choose to produce either 60 or 70 items. What is their profit for each case, and which level of production should they choose? Profit when producing 60 items =     Profit when producing 70 items =    Can you explain, from our model, why the company makes less profit when producing 10 more units?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
icon
Concept explainers
Question

For a certain company, the cost function for producing x items is C(x)=40x+100 and the revenue function for selling x items is R(x)=−0.5(x−100)2+5,000. The maximum capacity of the company is 150 items.

The profit function P(x) is the revenue function R(x) (how much it takes in)  minus the cost function C(x) (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(x)=   .

    Hint: Profit = Revenue - Cost as we examined in Discussion 3.

  1. What is the domain of P(x)?

    Hint: Does calculating P(x) make sense when x=−10 or x=1,000?

  2. The company can choose to produce either 60 or 70 items. What is their profit for each case, and which level of production should they choose?

    Profit when producing 60 items =    

    Profit when producing 70 items =   

  1. Can you explain, from our model, why the company makes less profit when producing 10 more units?
  2.  
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 30 images

Blurred answer
Knowledge Booster
Application of Differentiation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,