MARKET SHARE OF BOOKSTORES At a certain university, three bookstores-the University Bookstore, the Campus Bookstore, and the Book Mart-currently serve the university community. A survey conducted at the beg inning of the fall quarter found that the University Bookstore and the Campus Bookstore each had 40 % of the market, whereas the Book Mart had 20 % of the market. Each quarter, the University Bookstore retains 80 % of its customers but loses 10 % to the Campus Bookstore and 10 % to the Book Mart. The Campus Bookstore retains 75 % of its customers but loses 10 % to the University Bookstore and 15 % to the Book Mart. The Book Mart retains 90 % of its customers but loses 5 % to the University Bookstore and 5 % to the Campus Bookstore. If these trends continue, what percentage of the market will each store have at the beginning of the second quarter? The third quarter?

BuyFind

Finite Mathematics for the Manager...

12th Edition
Soo T. Tan
Publisher: Cengage Learning
ISBN: 9781337405782
BuyFind

Finite Mathematics for the Manager...

12th Edition
Soo T. Tan
Publisher: Cengage Learning
ISBN: 9781337405782

Solutions

Chapter 9.1, Problem 25E
Textbook Problem

MARKET SHARE OF BOOKSTORES At a certain university, three bookstores-the University Bookstore, the Campus Bookstore, and the Book Mart-currently serve the university community. A survey conducted at the beg inning of the fall quarter found that the University Bookstore and the Campus Bookstore each had 40 % of the market, whereas the Book Mart had 20 % of the market. Each quarter, the University Bookstore retains 80 % of its customers but loses 10 % to the Campus Bookstore and 10 % to the Book Mart. The Campus Bookstore retains 75 % of its customers but loses 10 % to the University Bookstore and 15 % to the Book Mart. The Book Mart retains 90 % of its customers but loses 5 % to the University Bookstore and 5 % to the Campus Bookstore. If these trends continue, what percentage of the market will each store have at the beginning of the second quarter? The third quarter?

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Chapter 9 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences
Ch. 9.1 - In Exercises 1-10, determine which of the matrices...Ch. 9.1 - In Exercises 1-10, determine which of the matrices...Ch. 9.1 - In Exercises 1-10, determine which of the matrices...Ch. 9.1 - The transition matrix for a Markov process is...Ch. 9.1 - The transition matrix for a Markov process is...Ch. 9.1 - The transition matrix for a Markov process is...Ch. 9.1 - The transition matrix for a Markov process is...Ch. 9.1 - In Exercises 1518, find X2 the probability...Ch. 9.1 - In Exercises 1518, find X2 the probability...Ch. 9.1 - In Exercises 1518, find X2 the probability...Ch. 9.1 - In Exercises 1518, find X2 the probability...Ch. 9.1 - Psychology Experiments: A psychologist conducts an...Ch. 9.1 - Small-town Revival: At the beginning of 2007, the...Ch. 9.1 - Political Polls: Morris Polling conducted a poll 6...Ch. 9.1 - Commuter Trends: In a large metropolitan area, 20...Ch. 9.1 - URBAN-SUBURBAN POPULATION FLOWRefer to Example 4....Ch. 9.1 - Taxi movement between zones: Refer to Example 6....Ch. 9.1 - MARKET SHARE OF BOOKSTORESAt a certain university,...Ch. 9.1 - MARKET SHARE OF AUTO MANUFACTURERES In a study of...Ch. 9.1 - Change of Majors by students: Records compiled by...Ch. 9.1 - Homeowners choice of Energy: A study conducted by...Ch. 9.1 - In Exercises 29 and 30, determine whether the...Ch. 9.1 - In Exercises 29 and 30, determine whether the...Ch. 9.1 - In Exercises 12, find X5 the probability...Ch. 9.1 - In Exercises 12, find X5 the probability...Ch. 9.1 - MARKET SHARE OF AUTO MANUFACTURERES Refer to...Ch. 9.1 - Market share of Bookstores: Refer to Exercise 25...Ch. 9.2 - What is a A steady state distribution vector, b a...Ch. 9.2 - How do you find the steady state distribution...Ch. 9.2 - In Exercises 1-8, determine which of the matrices...Ch. 9.2 - In Exercises 1-8, determine which of the matrices...Ch. 9.2 - In Exercises 1-8, determine which of the matrices...Ch. 9.2 - In Exercises 1-8, determine which of the matrices...Ch. 9.2 - In Exercises 1-8, determine which of the matrices...Ch. 9.2 - In Exercises 1-8, determine which of the matrices...Ch. 9.2 - In Exercises 1-8, determine which of the matrices...Ch. 9.2 - In Exercises 1-8, determine which of the matrices...Ch. 9.2 - In Exercises 9-16, find the steady state vector...Ch. 9.2 - In Exercises 9-16, find the steady state vector...Ch. 9.2 - In Exercise 9-16, find the steady state vector for...Ch. 9.2 - In Exercise 9-16, find the steady state vector for...Ch. 9.2 - In Exercise 9-16, find the steady state vector for...Ch. 9.2 - In Exercise 9-16, find the steady state vector for...Ch. 9.2 - In Exercise 9-16, find the steady state vector for...Ch. 9.2 - In Exercise 9-16, find the steady state vector for...Ch. 9.2 - PSYCHOLOGY EXPERIMENTS A psychologist conducts an...Ch. 9.2 - COMMUTER TRENDS Within a large metropolitan area,...Ch. 9.2 - ONE- AND TWO-INCOME FAMILIES From data compiled...Ch. 9.2 - PROFESSIONAL WOMEN From data compiled over a...Ch. 9.2 - BUYING TRENDS OF HOME BUYERS From data collected...Ch. 9.2 - HOMEOWNERS' CHOICE OF ENERGY A study conducted by...Ch. 9.2 - NETWORK NEWS VIEWERSHIP A television poll was...Ch. 9.2 - Network News Viewership Refer to Exercise 23 If...Ch. 9.2 - GENETICS In a certain species of roses, a plant...Ch. 9.2 - MARKET SHARE OF AUTO MANUFACTURERS In a study of...Ch. 9.2 - In Exercises 27 and 28, determine whether the...Ch. 9.2 - In Exercises 27 and 28, determine whether the...Ch. 9.2 - Let T be a regular stochastic matrix. Show that...Ch. 9.2 - In Exercises 1 and 2, find the steady state vector...Ch. 9.2 - In Exercise 1 and 2, find the steady state vector...Ch. 9.2 - Verify that the steady state vector for Example 4,...Ch. 9.3 - What is an absorbing stochastic matrix?Ch. 9.3 - Suppose that the absorbing stochastic matrix A has...Ch. 9.3 - In Exercise 1-8, determine whether the matrix is...Ch. 9.3 - In Exercise 1-8, determine whether the matrix is...Ch. 9.3 - In Exercise 1-8, determine whether the matrix is...Ch. 9.3 - In Exercise 1-8, determine whether the matrix is...Ch. 9.3 - In Exercise 1-8, determine whether the matrix is...Ch. 9.3 - In Exercise 1-8, determine whether the matrix is...Ch. 9.3 - In Exercise 1-8, determine whether the matrix is...Ch. 9.3 - In Exercise 1-8, determine whether the matrix is...Ch. 9.3 - In Exercises 9-14, rewrite each absorbing...Ch. 9.3 - In Exercises 9-14, rewrite each absorbing...Ch. 9.3 - In Exercises 9-14, rewrite each absorbing...Ch. 9.3 - In Exercises 9-14, rewrite each absorbing...Ch. 9.3 - In Exercises 9-14, rewrite each absorbing...Ch. 9.3 - In Exercises 9-14, rewrite each absorbing...Ch. 9.3 - In Exercise 15-24, compute the steady-state matrix...Ch. 9.3 - In Exercise 15-24, compute the steady-state matrix...Ch. 9.3 - In Exercise 15-24, compute the steady-state matrix...Ch. 9.3 - In Exercise 15-24, compute the steady-state matrix...Ch. 9.3 - In Exercise 15-24, compute the steady-state matrix...Ch. 9.3 - In Exercise 15-24, compute the steady-state matrix...Ch. 9.3 - In Exercise 15-24, compute the steady-state matrix...Ch. 9.3 - In Exercise 15-24, compute the steady-state matrix...Ch. 9.3 - In Exercise 15-24, compute the steady-state matrix...Ch. 9.3 - In Exercise 15-24, compute the steady-state matrix...Ch. 9.3 - BROADBAND INTERNET SERVICE As more and more people...Ch. 9.3 - GAME OF CHANCE Diane has decided to play the...Ch. 9.3 - GAME OF CHANCE Refer to Exercise 26. Suppose Diane...Ch. 9.3 - VIDEO RECORDERS Over the years, consumers turned...Ch. 9.3 - COLLEGE GRADUATION RATE: The registrar of...Ch. 9.3 - COURGE GRADUATION RATE The registrar of a law...Ch. 9.3 - GENETICS Refer to Example 4. If the offspring are...Ch. 9.3 - In Exercises 32 and 33, determine whether the...Ch. 9.3 - In Exercises 32 and 33, determine whether the...Ch. 9.4 - a. What is the maximin strategy for the row player...Ch. 9.4 - a. How do you find the saddle point in the payoff...Ch. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - GAME OF MATCHING FINGERS Robin and Cathy play a...Ch. 9.4 - MANAGEMENT DECISIONS Bradys, a conventional...Ch. 9.4 - FINANCIAL ANALYSIS The management of Acrosonic is...Ch. 9.4 - FINANCIAL ANALYSIS The proprietor of Belvederes is...Ch. 9.4 - MARKET SHARE: Rolands Barber Shop and Charleys...Ch. 9.4 - In Exercises 24-26, determine whether the...Ch. 9.4 - In Exercises 24-26, determine whether the...Ch. 9.4 - In Exercises 24-26, determine whether the...Ch. 9.5 - What does the expected value of a game measure?Ch. 9.5 - Suppose [abcd] is the payoff matrix for a...Ch. 9.5 - In Exercises 1-6, the payoff matrix and strategies...Ch. 9.5 - In Exercises 1-6, the payoff matrix and strategies...Ch. 9.5 - In Exercises 1-6, the payoff matrix and strategies...Ch. 9.5 - In Exercises 1-6, the payoff matrix and strategies...Ch. 9.5 - In Exercises 1-6, the payoff matrix and strategies...Ch. 9.5 - In Exercises 1-6, the payoff matrix and strategies...Ch. 9.5 - The payoff matrix for a game is given by [1223]...Ch. 9.5 - The payoff matrix for a game is given by...Ch. 9.5 - The payoff matrix for a game is [332311121] a....Ch. 9.5 - The payoff matrix for a game is [423422352] a....Ch. 9.5 - In Exercises 11-16, find the optimal strategies, P...Ch. 9.5 - In Exercises 11-16, find the optimal strategies, P...Ch. 9.5 - In Exercises 11-16, find the optimal strategies, P...Ch. 9.5 - In Exercises 11-16, find the optimal strategies, P...Ch. 9.5 - In Exercises 11-16, find the optimal strategies, P...Ch. 9.5 - In Exercises 11-16, find the optimal strategies, P...Ch. 9.5 - COIN-MATCHING GAME Consider the coin-matching game...Ch. 9.5 - INVESTMENT STRATEGIES As part of their investment...Ch. 9.5 - INVESTMENT STRATEGIES The Maxwells have decided to...Ch. 9.5 - CAMPAIGN STRATEGIES Bella Robinson and Steve...Ch. 9.5 - MARKETING STRATEGIES Two dentists, Lydia Russell...Ch. 9.5 - Let [a11a12a21a22] be the payoff matrix with a 22...Ch. 9.5 - Let [abcd] be the payoff matrix associated with a...Ch. 9.CRQ - Fill in the blanks. A Markov chain is a stochastic...Ch. 9.CRQ - Fill in the blanks. The outcome at any stage of...Ch. 9.CRQ - Fill in the blanks. The probabilities in a Markov...Ch. 9.CRQ - Fill in the blanks. A transition matrix associated...Ch. 9.CRQ - Fill in the blanks. If the probability...Ch. 9.CRQ - Fill in the blanks. A stochastic matrix T is a/an ...Ch. 9.CRQ - Fill in the blanks. In an absorbing stochastic...Ch. 9.CRQ - Fill in the blanks. a. A game in which the payoff...Ch. 9.CRQ - Fill in the blanks. A strategy that is most...Ch. 9.CRQ - Fill in the blanks. In a strictly determined game,...Ch. 9.CRE - In Exercise 14, determine which of the following...Ch. 9.CRE - In Exercise 14, determine which of the following...Ch. 9.CRE - In Exercise 14, determine which of the following...Ch. 9.CRE - In Exercise 14, determine which of the following...Ch. 9.CRE - In Exercise 5 and 6, find X2 the probability...Ch. 9.CRE - In Exercise 5 and 6, find X2 the probability...Ch. 9.CRE - In Exercises 7-10, determine whether the matrix is...Ch. 9.CRE - In Exercises 7-10, determine whether the matrix is...Ch. 9.CRE - In Exercises 7-10, determine whether the matrix is...Ch. 9.CRE - In Exercises 7-10, determine whether the matrix is...Ch. 9.CRE - In Exercises 11-14, find the steady-state matrix...Ch. 9.CRE - In Exercises 11-14, find the steady-state matrix...Ch. 9.CRE - In Exercises 11-14, find the steady-state matrix...Ch. 9.CRE - In Exercises 11-14, find the steady-state matrix...Ch. 9.CRE - URBANIZATION OF FARMLAND A study conducted by the...Ch. 9.CRE - AUTOMOBILE PREFERENCES: Auto Trend magazine...Ch. 9.CRE - In Exercises 1720, determine whether each game...Ch. 9.CRE - In Exercises 1720, determine whether each game...Ch. 9.CRE - In Exercises 1720, determine whether each game...Ch. 9.CRE - In Exercises 1720, determine whether each game...Ch. 9.CRE - In Exercise 21-24, find the expected payoff E of...Ch. 9.CRE - In Exercise 21-24, find the expected payoff E of...Ch. 9.CRE - In Exercise 21-24, find the expected payoff E of...Ch. 9.CRE - In Exercise 21-24, find the expected payoff E of...Ch. 9.CRE - In Exercise 25-28, find the optimal strategies, P...Ch. 9.CRE - In Exercise 25-28, find the optimal strategies, P...Ch. 9.CRE - In Exercise 25-28, find the optimal strategies, P...Ch. 9.CRE - In Exercise 25-28, find the optimal strategies, P...Ch. 9.CRE - COMPETITIVE PRICING Two competing music stores,...Ch. 9.CRE - OPTIMIZING DEMAND The management of a divison of...Ch. 9.BMO - The transition matrix for a Markov process is...Ch. 9.BMO - Find the steady-state vector for the transition...Ch. 9.BMO - Compute the steady-state matrix of the absorbing...Ch. 9.BMO - A two-person, zero-sum game is defined by the...Ch. 9.BMO - The payoff matrix for a certain game is A=[213234]...Ch. 9.BMO - The payoff matrix for a certain game is [3122] a....

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