6. Two players on a basketball team share playing time. Mark's expected number of points scored is SM(x) = 30x – 5x² if he plays the fraction x e [0,1] of the game. John's expected number is S(x) = 25x – 5x points if he plays the fraction x of the game. (i) Suppose that Mark plays the entire game. How many points does he expect to score? How many points would John expect to score if he played the fraction x = A of the game? Find the average scoring rate, S(A)/A, as A approaches zero. (ii) What fraction of the time should Mark play in order to maximize the total points scored by Mark and John? Find the expected number of points scored by each player per unit time.
6. Two players on a basketball team share playing time. Mark's expected number of points scored is SM(x) = 30x – 5x² if he plays the fraction x e [0,1] of the game. John's expected number is S(x) = 25x – 5x points if he plays the fraction x of the game. (i) Suppose that Mark plays the entire game. How many points does he expect to score? How many points would John expect to score if he played the fraction x = A of the game? Find the average scoring rate, S(A)/A, as A approaches zero. (ii) What fraction of the time should Mark play in order to maximize the total points scored by Mark and John? Find the expected number of points scored by each player per unit time.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Here is my question!
![6. Two players on a basketball team share playing time. Mark's expected number of points
scored is SM(x) = 30x – 5x² if he plays the fraction x e [0,1] of the game. John's expected
number is S(x) = 25x – 5x points if he plays the fraction x of the game.
(i) Suppose that Mark plays the entire game. How many points does he expect to score? How
many points would John expect to score if he played the fraction x = A of the game? Find the
average scoring rate, S(A)/A, as A approaches zero.
(ii) What fraction of the time should Mark play in order to maximize the total points scored by
Mark and John? Find the expected number of points scored by each player per unit time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ac87d00-6aaa-4f34-86ad-b7316a14f701%2F01e54871-beb3-4e00-9ea7-38eef495020a%2Fqsm0lca.png&w=3840&q=75)
Transcribed Image Text:6. Two players on a basketball team share playing time. Mark's expected number of points
scored is SM(x) = 30x – 5x² if he plays the fraction x e [0,1] of the game. John's expected
number is S(x) = 25x – 5x points if he plays the fraction x of the game.
(i) Suppose that Mark plays the entire game. How many points does he expect to score? How
many points would John expect to score if he played the fraction x = A of the game? Find the
average scoring rate, S(A)/A, as A approaches zero.
(ii) What fraction of the time should Mark play in order to maximize the total points scored by
Mark and John? Find the expected number of points scored by each player per unit time.
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 8 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education