4. The price p a book company charges for its most recent book is related to the demand q in weekly sales by the equation 100pq+q² = 5,000,000. Suppose the price is set at $40, which would make the demand 1,000 copies per week. a) Using implicit differentiation, compute the rate of change of demand with respect to price, and interpret the result. (Round the answer to two decimal places.)
4. The price p a book company charges for its most recent book is related to the demand q in weekly sales by the equation 100pq+q² = 5,000,000. Suppose the price is set at $40, which would make the demand 1,000 copies per week. a) Using implicit differentiation, compute the rate of change of demand with respect to price, and interpret the result. (Round the answer to two decimal places.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
2
![4.
The price p a book company charges for its most recent book is related
to the demand q in weekly sales by the equation
100pq+q² = 5,000,000.
Suppose the price is set at $40, which would make the demand 1,000 copies per week.
a) Using implicit differentiation, compute the rate of change of demand with respect to
price, and interpret the result. (Round the answer to two decimal places.)
b) Use the result of part (a) to compute the rate of change of revenue with respect to
price. Should the price be raised or lowered to increase revenue?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4cbb3a16-d911-4d4e-ac4a-559489c6b9b1%2F5735e2ba-022e-4360-a16e-e979cd04ddf1%2Fc7x680d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4.
The price p a book company charges for its most recent book is related
to the demand q in weekly sales by the equation
100pq+q² = 5,000,000.
Suppose the price is set at $40, which would make the demand 1,000 copies per week.
a) Using implicit differentiation, compute the rate of change of demand with respect to
price, and interpret the result. (Round the answer to two decimal places.)
b) Use the result of part (a) to compute the rate of change of revenue with respect to
price. Should the price be raised or lowered to increase revenue?
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)