For a certain company, the cost function for producing x items is C(x)=40x+200 and the revenue function for selling x items is R(x)=−0.5(x−80)2+3,200. The maximum capacity of the company is 140 items.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 40 or 50 items. What is their profit for each case, and which level of production should they choose?Profit when producing 40 items = Profit when producing 50 items = Can you explain, from our model, why the company makes less profit when producing 10 more units?

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Description: For a certain company, the cost function for producing x items is C(x)=40x+200 and the revenue function for selling x items is R(x)=−0.5(x−80)2+3,200. The maximum capacity of the company is 140 items.Answers to some of the questions are given below s

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Answered: For a certain company, the cost…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For a certain company, the cost function for producing x items is C(x)=40x+200 and the revenue function for selling x items is R(x)=−0.5(x−80)2+3,200. The maximum capacity of the company is 140 items.

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 40 or 50 items. What is their profit for each case, and which level of production should they choose?
Profit when producing 40 items =

Profit when producing 50 items =

Can you explain, from our model, why the company makes less profit when producing 10 more units?

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