of f(x) to dollars. Both functions have domain 1 ≤ x ≤ 25. (A) Sketch a graph of the revenue function in a rectangular coordinate system.

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...
icon
Related questions
Question
100%
Please help with #74
etween tire
ail market
y as a per-
of f(x) to
NOV
18
(A) Sketch a graph of the revenue function in a rectangular
coordinate system.
(B) Find the value of x that will produce the maximum rev-
enue. What is the maximum revenue?
(C) What is the wholesale price per chip that produces the
maximum revenue?
70. Revenue. The marketing research department for a company
that manufactures and sells notebook computers established
the following price-demand and revenue functions:
p(x) = 2,000 - 60x
R(x) = xp(x)
= = x(2,000 - 60x)
Price-demand function
Revenue function
where p(x) is the wholesale price in dollars at which x
thousand computers can be sold, and R(x) is in thousands of
dollars. Both functions have domain 1 ≤ x ≤ 25.
(A) Sketch a graph of the revenue function in a rectangular
coordinate system.
(B) Find the value of x that will produce the maximum
revenue. What is the maximum revenue to the nearest
thousand dollars?
(C) What is the wholesale price per computer (to the nearest
dollar) that produces the maximum revenue?
71. Break-even analysis. Use the revenue function from Prob-
tv
@
ST
66
Transcribed Image Text:etween tire ail market y as a per- of f(x) to NOV 18 (A) Sketch a graph of the revenue function in a rectangular coordinate system. (B) Find the value of x that will produce the maximum rev- enue. What is the maximum revenue? (C) What is the wholesale price per chip that produces the maximum revenue? 70. Revenue. The marketing research department for a company that manufactures and sells notebook computers established the following price-demand and revenue functions: p(x) = 2,000 - 60x R(x) = xp(x) = = x(2,000 - 60x) Price-demand function Revenue function where p(x) is the wholesale price in dollars at which x thousand computers can be sold, and R(x) is in thousands of dollars. Both functions have domain 1 ≤ x ≤ 25. (A) Sketch a graph of the revenue function in a rectangular coordinate system. (B) Find the value of x that will produce the maximum revenue. What is the maximum revenue to the nearest thousand dollars? (C) What is the wholesale price per computer (to the nearest dollar) that produces the maximum revenue? 71. Break-even analysis. Use the revenue function from Prob- tv @ ST 66
74. Profit-loss analysis. Use the revenue function from Problem
70 and the given cost function:
R(x) = x(2,000 - 60x)
C(x)
4,000 + 500x
Revenue function
Cost function
where x is thousands of computers, and R(x) and C(x)
are in thousands of dollars. Both functions have domain
1 ≤ x ≤ 25.
=
(A) Form a profit function P, and graph R, C, and P in the
same rectangular coordinate system.
(B) Discuss the relationship between the intersection points
of the graphs of R and C and the x intercepts of P.
(C) Find the x intercepts of P and the break-even points.
(D) Find the value of x that produces the maximum profit.
Find the maximum profit and compare with Problem 70B.
Transcribed Image Text:74. Profit-loss analysis. Use the revenue function from Problem 70 and the given cost function: R(x) = x(2,000 - 60x) C(x) 4,000 + 500x Revenue function Cost function where x is thousands of computers, and R(x) and C(x) are in thousands of dollars. Both functions have domain 1 ≤ x ≤ 25. = (A) Form a profit function P, and graph R, C, and P in the same rectangular coordinate system. (B) Discuss the relationship between the intersection points of the graphs of R and C and the x intercepts of P. (C) Find the x intercepts of P and the break-even points. (D) Find the value of x that produces the maximum profit. Find the maximum profit and compare with Problem 70B.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

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
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning