We found that the marketing research department for the company that manufactures and sells memory chips for microcomputers established the following price-demand and revenue functions: Pix) = 95 - 4x R(x) = xp(x) = x(95-4x) where p(x) is the wholesale price in dollars at which x million chips can be sold, and R(x) is in millions of dollars. Both functions have domain 1sxs 19. Price-demand function Revenue function .ww.. (A) Which of the following is the graph of the revenue function?
We found that the marketing research department for the company that manufactures and sells memory chips for microcomputers established the following price-demand and revenue functions: Pix) = 95 - 4x R(x) = xp(x) = x(95-4x) where p(x) is the wholesale price in dollars at which x million chips can be sold, and R(x) is in millions of dollars. Both functions have domain 1sxs 19. Price-demand function Revenue function .ww.. (A) Which of the following is the graph of the revenue function?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Price-Demand and Revenue Functions
We found that the marketing research department for the company that manufactures and sells memory chips for microcomputers established the following price-demand and revenue functions:
- **Price-demand function**: \( p(x) = 95 - 4x \)
- **Revenue function**: \( R(x) = xp(x) = x(95 - 4x) \)
Where \( p(x) \) is the wholesale price in dollars at which \( x \) million chips can be sold, and \( R(x) \) is in millions of dollars. Both functions have a domain of \( 1 \leq x \leq 19 \).
### Questions
**(A)** Which of the following is the graph of the revenue function?
- **Option A**: Graph shows a parabolic curve opening downwards with a vertex at around (10, 475).
- **Option B**: Graph shows a parabolic curve opening upwards.
- **Option C**: Graph shows a parabolic curve opening downwards with a vertex at around (10, 475).
**(B)** Find the output that will produce the maximum revenue.
- \[ \_\_\_\_\_ \] million chips (Type an integer or a fraction. Simplify your answer.)
What is the maximum revenue?
- \[ \_\_\_\_\_ \] million (Round to two decimal places.)
**(C)** What is the wholesale price per chip that produces the maximum revenue?
- \[ \$\_\_\_\_\_ \] (Round to the nearest dollar.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b904dad-beef-4dfd-8b79-df086fe59aa6%2F2e2fce81-8b1c-4624-9020-14f18d24cfac%2Fyv7nef_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Price-Demand and Revenue Functions
We found that the marketing research department for the company that manufactures and sells memory chips for microcomputers established the following price-demand and revenue functions:
- **Price-demand function**: \( p(x) = 95 - 4x \)
- **Revenue function**: \( R(x) = xp(x) = x(95 - 4x) \)
Where \( p(x) \) is the wholesale price in dollars at which \( x \) million chips can be sold, and \( R(x) \) is in millions of dollars. Both functions have a domain of \( 1 \leq x \leq 19 \).
### Questions
**(A)** Which of the following is the graph of the revenue function?
- **Option A**: Graph shows a parabolic curve opening downwards with a vertex at around (10, 475).
- **Option B**: Graph shows a parabolic curve opening upwards.
- **Option C**: Graph shows a parabolic curve opening downwards with a vertex at around (10, 475).
**(B)** Find the output that will produce the maximum revenue.
- \[ \_\_\_\_\_ \] million chips (Type an integer or a fraction. Simplify your answer.)
What is the maximum revenue?
- \[ \_\_\_\_\_ \] million (Round to two decimal places.)
**(C)** What is the wholesale price per chip that produces the maximum revenue?
- \[ \$\_\_\_\_\_ \] (Round to the nearest dollar.)
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