A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x)equals=74 comma 000 plus 80 x74,000+80x and p left parenthesis x right parenthesis equals 250 minus StartFraction x Over 20 EndFractionp(x)=250−x20, 0less than or equals≤xless than or equals≤50005000. (A) Find the maximum revenue. (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. (C) If the government decides to tax the company $66 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?
A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x)equals=74 comma 000 plus 80 x74,000+80x and p left parenthesis x right parenthesis equals 250 minus StartFraction x Over 20 EndFractionp(x)=250−x20, 0less than or equals≤xless than or equals≤50005000. (A) Find the maximum revenue. (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. (C) If the government decides to tax the company $66 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.CR: Chapter Review
Problem 70E: A company manufactures two fertilizers, x and y. Each 50-pound bag of fertilizer requires three...
Related questions
Topic Video
Question
A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are
C(x)equals=74 comma 000 plus 80 x74,000+80x
and
p left parenthesis x right parenthesis equals 250 minus StartFraction x Over 20 EndFractionp(x)=250−x20,
0less than or equals≤xless than or equals≤50005000.
(A) Find the maximum revenue.
(B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set.
(C) If the government decides to tax the company
$66
for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning