Linear Algebra and Its Applications (5th Edition)
5th Edition
ISBN: 9780321982384
Author: David C. Lay, Steven R. Lay, Judi J. McDonald
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 9.1, Problem 23E
Find the optimal strategies and the value of the game in Example 2.
EXAMPLE 2 Again suppose that each player has a supply of pennies, nickels, and dimes to play, but this time the payoff matrix is given as follows:
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Given the following Payoff Matrix:
Payoff Table - # of Avg Yards
Patriots choses (run) 50% of the time
Broncos
and choses (pass) 50% of the time
Run
Pass
Run
3
Broncos choses (run) 40% of the time
Patriots
Pass
and choses (pass) 60% of the time
1
Hhow many yards can Patriots expect to gain per 100 plays?
Patriots
e 25-20. Given the following payoff matrix :
Payoff (in Rs.)
State of Nature
Act
Cold Weather
Hot Weather
Sell Cold Drinks
50
100
Sell Hot Drinks
120
40
and given the probability of weather being hot is 0-8, set up the opportunity loss table and compute
opportunity loss of each action. Select the best act.
An investor plans to put $50,000 in one of four investments. The return on each
investment depends on whether next year's economy is strong or weak. The
following table summarizes the possible payoffs, in dollars, for the four
investments.
Certificate
of deposit
Office
complex
Land
speculation
Technical
school
Next year's economy
Strong
7,000
15,000
32,500
6,000
Weak
7,000
4,500
- 17,000
12,000
Let V, W, X, and Y denote the payoffs for the certificate of deposit,
office complex, land speculation, and technical school, respectively.
Then V, W, X, and Y are random variables. Assume that next year's
economy has a 30% chance of being strong and a 70% chance of being
weak.
a. Find the probability distribution of each random variable V, W, X, and
Y.
What is the probability distribution for V?
V
7,000
P(V=v)
Chapter 9 Solutions
Linear Algebra and Its Applications (5th Edition)
Ch. 9.1 - Find the optimal strategies and the value of the...Ch. 9.1 - Player R has a supply of dimes and quarters....Ch. 9.1 - Prob. 2ECh. 9.1 - In the traditional Japanese childrens game janken...Ch. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Find all saddle points for the matrix games in...Ch. 9.1 - Find all saddle points for the matrix games in...Ch. 9.1 - Find all saddle points for the matrix games in...Ch. 9.1 - Prob. 9E
Ch. 9.1 - Prob. 10ECh. 9.1 - In Exercises 11-18, find the optimal row and...Ch. 9.1 - In Exercises 11-18, find the optimal row and...Ch. 9.1 - In Exercises 11-18, find the optimal row and...Ch. 9.1 - In Exercises 11-18, find the optimal row and...Ch. 9.1 - In Exercises 11-18, find the optimal row and...Ch. 9.1 - Prob. 16ECh. 9.1 - In Exercises 11-18, find the optimal row and...Ch. 9.1 - In Exercises 11-18, find the optimal row and...Ch. 9.1 - In Exercises 21 and 22, mark each statement True...Ch. 9.1 - In Exercises 21 and 22, mark each statement True...Ch. 9.1 - Find the optimal strategies and the value of the...Ch. 9.1 - Bill and Wayne are playing a game in which each...Ch. 9.1 - Consider the matrix game A=[abcd] where A has no...Ch. 9.2 - Consider the following problem: Maximize 2x1 + x2...Ch. 9.2 - Graph the feasible set for Practice Problem 1.Ch. 9.2 - Find the extreme points of the feasible set in...Ch. 9.2 - Use the answer to Practice Problem 3 to find the...Ch. 9.2 - Betty plans to invest a total of 12,000 in mutual...Ch. 9.2 - A dog breeder decides to feed his dogs a...Ch. 9.2 - In Exercises 3-6, find vectors b and c and matrix...Ch. 9.2 - In Exercises 3-6, find vectors b and c and matrix...Ch. 9.2 - In Exercises 3-6, find vectors b and c and matrix...Ch. 9.2 - In Exercises 3-6, find vectors b and c and matrix...Ch. 9.2 - In Exercises 7-10, solve the linear programming...Ch. 9.2 - In Exercises 7-10, solve the linear programming...Ch. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.3 - Use the simplex method to solve the following...Ch. 9.3 - In Exercises 1 and 2, set up the initial simplex...Ch. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Exercises 7 and 8 relate to a canonical linear...Ch. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Solve Exercises 9-14 by using the simplex method....Ch. 9.3 - Solve Exercises 9-14 by using the simplex method...Ch. 9.3 - Solve Exercises 9-14 by using the simplex method....Ch. 9.3 - Solve Example 7 by bringing x1 into the solution...Ch. 9.3 - Use the simplex method to solve the linear...Ch. 9.3 - Prob. 17ECh. 9.3 - Use the simplex method to solve the linear...Ch. 9.4 - The following questions relate to the Shady-Lane...Ch. 9.4 - The following questions relate to the Shady-Lane...Ch. 9.4 - Prob. 3PPCh. 9.4 - Prob. 1ECh. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - In Exercises 1-4, state the dual of the given...Ch. 9.4 - In Exercises 5-8, use the final tableau in the...Ch. 9.4 - In Exercises 5-8, use the final tableau in the...Ch. 9.4 - In Exercises 5-8, use the final tableau in the...Ch. 9.4 - In Exercises 5-8, use the final tableau in the...Ch. 9.4 - Exercises 9 and 10 relate to a primal linear...Ch. 9.4 - Sometimes a minimization problem has inequalities...Ch. 9.4 - Sometimes a minimization problem has inequalities...Ch. 9.4 - Sometimes a minimization problem has inequalities...Ch. 9.4 - Sometimes a minimization problem has inequalities...Ch. 9.4 - Exercises 15 and 16 refer to Exercise 15 in...Ch. 9.4 - Exercises 15 and 16 refer to Exercise 15 in...Ch. 9.4 - Solve the matrix games in Exercises 17 and 18 by...Ch. 9.4 - Solve the matrix games in Exercises 17 and 18 by...Ch. 9.4 - Solve the matrix game in Exercise 9 in Section 9.1...Ch. 9.4 - Solve the matrix game in Exercise 10 in Section...Ch. 9.4 - Prob. 22ECh. 9.4 - Prob. 23E
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table. Labor-Hours per Ski Maximum Labor-Hours Available per Day Department Fabricating Finishing Answer parts (A), (B), and (C) below. Trick Ski 6 1 Slalom Ski 4 1 (A) If the profit on a trick ski is $30 and the profit on a slalom ski is $40, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit? The maximum profit is $ The maximum occurs when trick skis and 216 42 slalom skis are produced.arrow_forwardDuffin House, Higgins Press, and Sickle Publications all went public on the same day recently. John O'Hagan had the opportunity to participate in all three initial public offerings (partly because he and Marjory Duffin are good friends). He made a considerable profit when he sold all of the stock 2 days later on the open market. The following table shows the purchase price and percentage yield on the investment in each company. Purchase Priceper Share ($) Yield (%) Duffin House (DHS) 8 20 Higgins Press (HPR) 10 15 Sickle Publications (SPUB) 15 15 He invested $25,000 in a total of 2,600 shares and made a $4,350 profit from the transactions. How many shares in each company did he purchase? Duffin House shares Higgins Press shares Sickle Publications shares I have x+y+z=2600 8x+10y+15z=25,000 160x+150y+225z=435,000 i keep getting y=506, i know im doing something wrong :(arrow_forwardsee imagearrow_forward
- The following question is based on the following information about the stocks of KT Corporation, International Flavors & Fragrances, and Quality Systems. Price Dividend Yield KT (KT Corporation) $16 7% IFF (InternationalFlavors & Fragrances) $56 2% QSII (Quality Systems) $80 2% You invested a total of $11,600 in shares of the three stocks at the given prices, and expected to earn $272 in annual dividends. If you purchased a total of 200 shares, how many shares of each stock did you purchase? KT IFF QSIIarrow_forwardA ticket between Corellia and Dantooine (located in a galaxy far far away) sells for $150. The plane can hold 100 people. It costs $8000 to fly an empty plane. Each person on the plane incurs variable costs of $30 (for food and fuel). If the flight is overbooked, anyone who cannot get a seat receives $300 in compensation. On average, 95% of all people who have a reservation show up for the flight. To maximize profit, how many reservations for the flight should you book? Hint: You can assume that the number of people that show up for a flight follows a binomial random variable.arrow_forward15. Please help with game matrix. Percentages A= 40% B=50% c=10%arrow_forward
- Qd 116.arrow_forwardNeeds Complete solution with 100 % accuracy.arrow_forwardIf the Round Game had been discontinued before the last quarter, what would operating income have been for the company as a whole? Operating income without round $__________ Twinkie Trivia Co. manufactures and sells two trivia products, the Square Trivia Game and the Round Trivia Game. Last quarter’s operating profits, by product, and for the company as a whole, were as follows: Square Round Total Sales revenue $11,000 $6,600 $17,600 Variable expenses 4,400 3,000 7,400 Contribution margin 6,600 3,600 10,200 Fixed expenses 2,750 4,200 6,950 Operating income $ 3,850 $(600) $ 3,250 Forty percent of the Round Game’s fixed costs could have been avoided if the game had not been produced or soldarrow_forward
- Two-Finger Morra is a game in which two players each hold up one or two fingers. The payoff, in dollars, is the total number of fingers shown. R receives the payoff if the total is even, and C receives the payoff if the total is odd. Write the payoff matrix. C Rarrow_forwardA politician can emphasize jobs or the environment in her election campaign. The voters can be concerned about jobs or the environment. A payoff matrix showing the utility of each possible outcome is shown. The political analysts feel there is a 0.51 chance that the voters will emphasize jobs. Voters Jobs Environment +25 Jobs - 10 Environment - 15 +30 Which strategy should the candidate adopt? What is the expected utility? Which should the candidate emphasize to gain the highest utility? Jobs Environment What is the expected utility of the strategy chosen in the previous step? 7.05 (Type an integer or a decimal.)arrow_forwardFind the optimal strategies, P and Q, for the row and column players, respectively. -2 3 1 -3 P = Q= Compute the expected payoff E of the matrix game if the players use their optimal strategies. (Round your answer to two decimal places.) E = Which player does the game favor, if any? OR O C Oneitherarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education
Solve ANY Optimization Problem in 5 Steps w/ Examples. What are they and How do you solve them?; Author: Ace Tutors;https://www.youtube.com/watch?v=BfOSKc_sncg;License: Standard YouTube License, CC-BY
Types of solution in LPP|Basic|Multiple solution|Unbounded|Infeasible|GTU|Special case of LP problem; Author: Mechanical Engineering Management;https://www.youtube.com/watch?v=F-D2WICq8Sk;License: Standard YouTube License, CC-BY
Optimization Problems in Calculus; Author: Professor Dave Explains;https://www.youtube.com/watch?v=q1U6AmIa_uQ;License: Standard YouTube License, CC-BY
Introduction to Optimization; Author: Math with Dr. Claire;https://www.youtube.com/watch?v=YLzgYm2tN8E;License: Standard YouTube License, CC-BY