تكلم مع الذكاء الاصطناعي
Deck 11: Games and Decisions
ملء الشاشة (f)
سؤال
Is the following matrix game strictly determined?
سؤال
Is the following matrix game strictly determined?
سؤال
Is the following matrix game strictly determined?
سؤال
Is the following matrix game strictly determined?
سؤال
The matrix for a strictly determined matrix game is given below. Determine if the game is fair or not fair. 
A) Fair
B) Not fair
A) Fair
B) Not fair
سؤال
The matrix for a strictly determined matrix game is given below. Determine if the game is fair or not fair. 
A) Fair
B) Not fair
A) Fair
B) Not fair
سؤال
Find the saddle values, if it exists, for the matrix game (include row and column location). 
A) 6; row 1 column 2
B) 4; row 1 column 1
C) 3; row 2 column 1
D) 4; row 2 column 1
A) 6; row 1 column 2
B) 4; row 1 column 1
C) 3; row 2 column 1
D) 4; row 2 column 1
سؤال
Find the saddle values, if it exists, for the matrix game (include row and column location). 
A) 2; row 2 column 1
B) 2; row 3 column 2
C) 1; row 1 column 2
D) Does not exist
A) 2; row 2 column 1
B) 2; row 3 column 2
C) 1; row 1 column 2
D) Does not exist
سؤال
Find the saddle values, if it exists, for the matrix game (include row and column location). 
A) -5; row 1 column 2
B) 6; row 2 column 1
C) -2; row 3 column 2
D) -4; row 2 column 2
A) -5; row 1 column 2
B) 6; row 2 column 1
C) -2; row 3 column 2
D) -4; row 2 column 2
سؤال
Find the saddle values, if it exists, for the matrix game (include row and column location). 
A) 0; row 3 column 4
B) 4; row 3 column 1
C) 0; row 1 column 2
D) 3; row 1 column 1
A) 0; row 3 column 4
B) 4; row 3 column 1
C) 0; row 1 column 2
D) 3; row 1 column 1
سؤال
Find the saddle value, if it exists, for the matrix game (include row and column location). 
A) 1; row 1 column 3
B) 3; row 3 column 1
C) 1; row 3 column 2
D) 3; row 1 column 1
A) 1; row 1 column 3
B) 3; row 3 column 1
C) 1; row 3 column 2
D) 3; row 1 column 1
سؤال
What is the optimal strategy for each player in the following matrix game? Use R for row and C for column. 
A) R plays row 2 or row 3, C plays column 1
B) R plays row 2, C plays column 4
C) R plays row 1 , C plays column 2
D) R plays row 1 or row 2, C plays column 1
A) R plays row 2 or row 3, C plays column 1
B) R plays row 2, C plays column 4
C) R plays row 1 , C plays column 2
D) R plays row 1 or row 2, C plays column 1
سؤال
Daisy and Gus write down one of the numbers 1, 4 , or 7. If the sum of the numbers is even Daisy pays Gus that number of dimes. If the sum of the numbers is odd, Gus pays Daisy that number of dimes. Write Daisy's game matrix that corresponds to this situation.
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Find the saddle point and value of the game:
-Suppose a rugby team with the ball (team A) can choose from three plays while the opposing team (B) has four possible defenses. The numbers in the payoff matrix represent yards gained by A.
A) (3, 4), value 6
B) (1, 1), value 15
C) (2, 2), value 18
D) (2, 3), value 5
-Suppose a rugby team with the ball (team A) can choose from three plays while the opposing team (B) has four possible defenses. The numbers in the payoff matrix represent yards gained by A.
A) (3, 4), value 6
B) (1, 1), value 15
C) (2, 2), value 18
D) (2, 3), value 5
سؤال
Two countries are involved in a border war. Each country has 3 strategies with payoffs in square miles of land. Positive numbers represent gains by A.
A) (3, 2), value 5
B) (1, 3), value -10
C) (3, 3), value -10
D) (1, 3), value -8
A) (3, 2), value 5
B) (1, 3), value -10
C) (3, 3), value -10
D) (1, 3), value -8
سؤال
Two merchants in the same city plan on selling a new product. Each merchant has 3 strategies to enhance sales. The strategies chosen by each will determine the percentage of sales of the product each gets.
A) (1, 2), value -10
B) (1, 1), value -53
C) (2, 2), value 12
D) (3, 1), value -51
A) (1, 2), value -10
B) (1, 1), value -53
C) (2, 2), value 12
D) (3, 1), value -51
سؤال
Determine which row(s) and column(s) of the game matrix are recessive.
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Delete recessive rows and columns from the following matrix game:
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Delete recessive rows and columns from the following matrix game:
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Find the value of the game.
-
A)
B)
C)
D)
-
A)
B)
C)
D)
سؤال
Find the expected value of the matrix game M = 
for the respective row and column strategies:
A)
B)
C) -
D)
for the respective row and column strategies:A)
B)
C) -
D)
سؤال
Find the expected value of the matrix game M = 
for the respective row and column strategies:
A) 1
B)
C)
D)
for the respective row and column strategies:A) 1
B)
C)
D)
سؤال
Find the expected value of the game matrix A = 
if player 1 and player 2 decide on strategies
A) 1
B)
C)
D)
if player 1 and player 2 decide on strategiesA) 1
B)
C)
D)
سؤال
Find the expected value of the game matrix A = 
if player 1 and player 2 decide on strategies 
and Q = 
.
A)
B)
C)
D)
if player 1 and player 2 decide on strategies and Q = .A)
B)
C)
D)
سؤال
Find the expected value of the game matrix A = 
if player 1 and player 2 decide on strategies 
and Q = 
.
A)
B)
C)
D)
if player 1 and player 2 decide on strategies and Q = .A)
B)
C)
D)
سؤال
Solve the matrix game M = 
indicating optimal strategies 
and 
for R and C respectively, and the value v of the game.
A)
B)
C)
D)
indicating optimal strategies and for R and C respectively, and the value v of the game.A)
B)
C)
D)
سؤال
سؤال
سؤال
In a two-finger Morra game, if player R matches player C, then R wins and if R and C don't match, then C wins. R will win $3 with one finger or two fingers, while C will win $1 with one finger and $5 with 2 fingers. The payoff matrix is 
Find the optimal strategies 
and 
for R and C respectively, and the value v of the game.
A)
B)
C)
D)
Find the optimal strategies and for R and C respectively, and the value v of the game.A)
B)
C)
D)
سؤال
Two supermarkets, R and C, want to run a promotional on the same item. A market research firm provided the payoff matrix below, where each entry indicates the percentage of customers going to market R at the indicated prices of that item. Find the saddle value, and the optimum strategy for each store.
A) 60%; R sells the item at $1.85, C sells the item at $1.55.
B) 60%; R sells the item at $1.55, C sells the item at $1.85.
C) 50%; R sells the item at $1.85, C sells the item at $1.55.
D) 50%; R sells the item at $1.55, C sells the item at $1.85.
A) 60%; R sells the item at $1.85, C sells the item at $1.55.
B) 60%; R sells the item at $1.55, C sells the item at $1.85.
C) 50%; R sells the item at $1.85, C sells the item at $1.55.
D) 50%; R sells the item at $1.55, C sells the item at $1.85.
سؤال
QMC decided to put its new product on the market with ads in a trade magazine and a booth at a trade show. It found out that its major competitor ZMC also had decided to advertise the same way for its new product. The payoff matrix shows the increased sales for QMC, as well as decreased sales for ZMC. What is the optimum strategy for QMC and the value of the game? 
A) QMC should use ads with probabilityand use booths with probability
. The value of the game is 
. 
B) QMC should use ads with probabilityand use booths with probability
. The value of the game is 
. 
A) QMC should use ads with probabilityand use booths with probability
. The value of the game is . B) QMC should use ads with probabilityand use booths with probability
. The value of the game is . سؤال
Two Wally-Worlds are going to build within a three block area. The exact sites will determine the percentage of business above or below 50% each gets, as shown in the payoff matrix. What is the value of the game?
A) 12
B) 6
C) 8
D) 11
A) 12
B) 6
C) 8
D) 11
سؤال
Two racquetball clubs are in competition in attracting new members. Advertising campaigns are being contemplated by both clubs which emphasize either beginning, intermediate, or advanced player tournaments among members. After careful research, the following results were found:
Thus, if beginner tournaments are featured by both clubs, Club A expects to attract 25% of the new members and Club B expects to attract 75% of the new members, etc. Find the value of the game.
A) 55%
B) 85%
C) 45%
D) 65%
Thus, if beginner tournaments are featured by both clubs, Club A expects to attract 25% of the new members and Club B expects to attract 75% of the new members, etc. Find the value of the game.
A) 55%
B) 85%
C) 45%
D) 65%
سؤال
The U.S. Marines is playing a war game with side A trying to capture side B's headquarters. Side A has three strategies and side B has four defenses. The payoff matrix shows side A's percentage chance of winning. What is the value of the game?
A) -75
B) -21
C) -41
D) 51
A) -75
B) -21
C) -41
D) 51
سؤال
Find the smallest integer k ? 0 such that adding k to each entry of the given matrix produces a matrix with all positive payoffs:
-
A) 4
B) 2
C) 1
D) 3
-
A) 4
B) 2
C) 1
D) 3
سؤال
Find the smallest integer k ? 0 such that adding k to each entry of the given matrix produces a matrix with all positive payoffs:
-
A) 3
B) 2
C) 0
D) 1
-
A) 3
B) 2
C) 0
D) 1
سؤال
Suppose a matrix game has the following nonstrictly determined matrix:
Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.
A)
B)
Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.
A)
B)
سؤال
Suppose a matrix game has the following nonstrictly determined matrix:
Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.
A)
B)
Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.
A)
B)
سؤال
Suppose a matrix game has the following nonstrictly determined matrix:
Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.
A)
B)
Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.
A)
B)
سؤال
Solve the matrix game using a geometric linear programming approach.
M =
A)
B)
C)
D)
M =
A)
B)
C)
D)
سؤال
سؤال
سؤال
A small town has two competing grocery stores, store R and store C. Each week each store decides to advertise its specials using either a newspaper advertisement or a mailing. The following payoff matrix indicates the percentage of market gain or loss for each choice of action by store R and store C.
Use linear programming and a geometric approach to find optimal strategies
and 
for store R and store C and the value v of the game.
A)
B)
C)
D)
Use linear programming and a geometric approach to find optimal strategies
and for store R and store C and the value v of the game.A)
B)
C)
D)
سؤال
Use the simplex method to find the optimum strategy for players A and B and the value of the game for the payoff matrix:
-
A)
B)
C)
D)
-
A)
B)
C)
D)
سؤال
Use the simplex method to find the optimum strategy for players A and B and the value of the game for the payoff matrix:
-
A)
B)
C)
D)
-
A)
B)
C)
D)
سؤال
Use the simplex method to find the optimum strategy for players A and B and the value of the game for the payoff matrix:
-
A)
B)
C)
D)
-
A)
B)
C)
D)
سؤال
Use the simplex method to find the optimum strategy for players A and B and the value of the game for the payoff matrix:
-
A)
B)
C)
D)
-
A)
B)
C)
D)
سؤال
A company has three different marketing strategies that produce different results depending upon whether inflation is above 6%, between 3% and 6% inclusive, or below 3% annually. The experts cannot predict inflation for the next year. The company has three plans of action and will implement these at varying percentages of its total operation. The payoff matrix for these three plans is given below, with values given in hundred thousands. What is the market strategy for the company that will yield the best expected value? 
A) The company should use Plan 1 with probability 4/13, Plan 2 with probability 9/13, and Plan 3 with probability 0.
B) The company should use Plan 1 with probability 5/13, Plan 2 with probability 8/13, and Plan 3 with probability 0.
C) The company should use Plan 1 with probability 1, Plan 2 with probability 0, and Plan 3 with probability 0.
D) The company should use Plan 1 with probability 0, Plan 2 with probability 1, and Plan 3 with probability 0.
A) The company should use Plan 1 with probability 4/13, Plan 2 with probability 9/13, and Plan 3 with probability 0.
B) The company should use Plan 1 with probability 5/13, Plan 2 with probability 8/13, and Plan 3 with probability 0.
C) The company should use Plan 1 with probability 1, Plan 2 with probability 0, and Plan 3 with probability 0.
D) The company should use Plan 1 with probability 0, Plan 2 with probability 1, and Plan 3 with probability 0.
سؤال
A company has three different marketing strategies that produce different results depending upon whether inflation is above 6%, between 3% and 6% inclusive, or below 3% annually. The experts cannot predict inflation for the next year. The company has three plans of action and will implement these at varying percentages of its total operation. The payoff matrix for these three plans is given below, with values given in hundred thousands. What is the marketing strategy for the company that will yield the best expected value? 
A) The company should use Plan 1 with probability 1/3, Plan 2 with probability 1/3, and Plan 3 with probability 1/3.
B) The company should use Plan 1 with probability 0, Plan 2 with probability 1, and Plan 3 with probability 0.
C) The company should use Plan 1 with probability 1, Plan 2 with probability 0, and Plan 3 with probability 0.
D) The company should use Plan 1 with probability 5/13, Plan 2 with probability 0, and Plan 3 with probability 8/13.
A) The company should use Plan 1 with probability 1/3, Plan 2 with probability 1/3, and Plan 3 with probability 1/3.
B) The company should use Plan 1 with probability 0, Plan 2 with probability 1, and Plan 3 with probability 0.
C) The company should use Plan 1 with probability 1, Plan 2 with probability 0, and Plan 3 with probability 0.
D) The company should use Plan 1 with probability 5/13, Plan 2 with probability 0, and Plan 3 with probability 8/13.
سؤال
A company has three products that fluctuate in favorability. The payoff matrix for the expected profit in tens of thousands of dollars is given below. What are the percentages of each product that the company should make that would maximize the expected value of the profit? Round to the nearest tenth of a percent, if necessary. 
A) Product 1: 0%, Product 2: 100%, Product 3: 0%
B) Product 1: 38.5%, Product 2: 0%, Product 3: 61.5%
C) Product 1: 100%, Product 2: 0%, Product 3: 0%
D) Product 1: 33.3%, Product 2: 33.3%, Product 3: 33.3%
A) Product 1: 0%, Product 2: 100%, Product 3: 0%
B) Product 1: 38.5%, Product 2: 0%, Product 3: 61.5%
C) Product 1: 100%, Product 2: 0%, Product 3: 0%
D) Product 1: 33.3%, Product 2: 33.3%, Product 3: 33.3%
سؤال
A person has hired an investment broker to buy stock. The broker has three different stock funds that are of interest, but each is sensitive to a certain economic indicator that is impossible to predict. The indicator will be positive, neutral, or negative. The table below shows the payoffs in thousands of dollars. Find the strategy that the broker should recommend to maximize the expected value of the investment. 
A) Invest in Stock A with probability 1, invest in Stock B with probability 0, and invest in Stock C with probability 0.
B) Invest in Stock A with probability 5/13, invest in Stock B with probability 8/13, and invest in Stock C with probability 0.
C) Invest in Stock A with probability 4/13, invest in Stock B with probability 9/13, and invest in Stock C with probability 0.
D) Invest in Stock A with probability 0, invest in Stock B with probability 1, and invest in Stock C with probability 0.
A) Invest in Stock A with probability 1, invest in Stock B with probability 0, and invest in Stock C with probability 0.
B) Invest in Stock A with probability 5/13, invest in Stock B with probability 8/13, and invest in Stock C with probability 0.
C) Invest in Stock A with probability 4/13, invest in Stock B with probability 9/13, and invest in Stock C with probability 0.
D) Invest in Stock A with probability 0, invest in Stock B with probability 1, and invest in Stock C with probability 0.
سؤال
A person is considering three different stocks, and each is sensitive to a certain economic indicator. The indicator will be positive, neutral, or negative, and fluctuate randomly. The payoffs are given in the table below, in thousands of dollars. What investment strategy should the person make to obtain the best expected value of profit? 
A) Invest in Stock A with probability 1/3, invest in Stock B with probability 1/3, and invest in Stock C with probability 1/3.
B) Invest in Stock A with probability 5/13, invest in Stock B with probability 0, and invest in Stock C with probability 8/13.
C) Invest in Stock A with probability 0, invest in Stock B with probability 1, and invest in Stock C with probability 0.
D) Invest in Stock A with probability 1, invest in Stock B with probability 0, and invest in Stock C with probability 0.
A) Invest in Stock A with probability 1/3, invest in Stock B with probability 1/3, and invest in Stock C with probability 1/3.
B) Invest in Stock A with probability 5/13, invest in Stock B with probability 0, and invest in Stock C with probability 8/13.
C) Invest in Stock A with probability 0, invest in Stock B with probability 1, and invest in Stock C with probability 0.
D) Invest in Stock A with probability 1, invest in Stock B with probability 0, and invest in Stock C with probability 0.
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ملء الشاشة (f)
Deck 11: Games and Decisions
1
Is the following matrix game strictly determined?
False
2
Is the following matrix game strictly determined?
True
3
Is the following matrix game strictly determined?
True
4
Is the following matrix game strictly determined?
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5
The matrix for a strictly determined matrix game is given below. Determine if the game is fair or not fair.
A) Fair
B) Not fair
A) Fair
B) Not fair
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6
The matrix for a strictly determined matrix game is given below. Determine if the game is fair or not fair.
A) Fair
B) Not fair
A) Fair
B) Not fair
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7
Find the saddle values, if it exists, for the matrix game (include row and column location).
A) 6; row 1 column 2
B) 4; row 1 column 1
C) 3; row 2 column 1
D) 4; row 2 column 1
A) 6; row 1 column 2
B) 4; row 1 column 1
C) 3; row 2 column 1
D) 4; row 2 column 1
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8
Find the saddle values, if it exists, for the matrix game (include row and column location).
A) 2; row 2 column 1
B) 2; row 3 column 2
C) 1; row 1 column 2
D) Does not exist
A) 2; row 2 column 1
B) 2; row 3 column 2
C) 1; row 1 column 2
D) Does not exist
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9
Find the saddle values, if it exists, for the matrix game (include row and column location).
A) -5; row 1 column 2
B) 6; row 2 column 1
C) -2; row 3 column 2
D) -4; row 2 column 2
A) -5; row 1 column 2
B) 6; row 2 column 1
C) -2; row 3 column 2
D) -4; row 2 column 2
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10
Find the saddle values, if it exists, for the matrix game (include row and column location).
A) 0; row 3 column 4
B) 4; row 3 column 1
C) 0; row 1 column 2
D) 3; row 1 column 1
A) 0; row 3 column 4
B) 4; row 3 column 1
C) 0; row 1 column 2
D) 3; row 1 column 1
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11
Find the saddle value, if it exists, for the matrix game (include row and column location).
A) 1; row 1 column 3
B) 3; row 3 column 1
C) 1; row 3 column 2
D) 3; row 1 column 1
A) 1; row 1 column 3
B) 3; row 3 column 1
C) 1; row 3 column 2
D) 3; row 1 column 1
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12
What is the optimal strategy for each player in the following matrix game? Use R for row and C for column.
A) R plays row 2 or row 3, C plays column 1
B) R plays row 2, C plays column 4
C) R plays row 1 , C plays column 2
D) R plays row 1 or row 2, C plays column 1
A) R plays row 2 or row 3, C plays column 1
B) R plays row 2, C plays column 4
C) R plays row 1 , C plays column 2
D) R plays row 1 or row 2, C plays column 1
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13
Daisy and Gus write down one of the numbers 1, 4 , or 7. If the sum of the numbers is even Daisy pays Gus that number of dimes. If the sum of the numbers is odd, Gus pays Daisy that number of dimes. Write Daisy's game matrix that corresponds to this situation.
A)
B)
C)
D)
A)
B)
C)
D)
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14
Find the saddle point and value of the game:
-Suppose a rugby team with the ball (team A) can choose from three plays while the opposing team (B) has four possible defenses. The numbers in the payoff matrix represent yards gained by A.
A) (3, 4), value 6
B) (1, 1), value 15
C) (2, 2), value 18
D) (2, 3), value 5
-Suppose a rugby team with the ball (team A) can choose from three plays while the opposing team (B) has four possible defenses. The numbers in the payoff matrix represent yards gained by A.
A) (3, 4), value 6
B) (1, 1), value 15
C) (2, 2), value 18
D) (2, 3), value 5
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15
Two countries are involved in a border war. Each country has 3 strategies with payoffs in square miles of land. Positive numbers represent gains by A.
A) (3, 2), value 5
B) (1, 3), value -10
C) (3, 3), value -10
D) (1, 3), value -8
A) (3, 2), value 5
B) (1, 3), value -10
C) (3, 3), value -10
D) (1, 3), value -8
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16
Two merchants in the same city plan on selling a new product. Each merchant has 3 strategies to enhance sales. The strategies chosen by each will determine the percentage of sales of the product each gets.
A) (1, 2), value -10
B) (1, 1), value -53
C) (2, 2), value 12
D) (3, 1), value -51
A) (1, 2), value -10
B) (1, 1), value -53
C) (2, 2), value 12
D) (3, 1), value -51
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17
Determine which row(s) and column(s) of the game matrix are recessive.
A)
B)
C)
D)
A)
B)
C)
D)
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18
Delete recessive rows and columns from the following matrix game:
A)
B)
C)
D)
A)
B)
C)
D)
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19
Delete recessive rows and columns from the following matrix game:
A)
B)
C)
D)
A)
B)
C)
D)
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20
Find the value of the game.
-
A)
B)
C)
D)
-
A)
B)
C)
D)
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21
Find the expected value of the matrix game M = for the respective row and column strategies:
A)
B)
C) -
D)
for the respective row and column strategies:A)
B)
C) -
D)
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22
Find the expected value of the matrix game M = for the respective row and column strategies:
A) 1
B)
C)
D)
for the respective row and column strategies:A) 1
B)
C)
D)
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23
Find the expected value of the game matrix A = if player 1 and player 2 decide on strategies
A) 1
B)
C)
D)
if player 1 and player 2 decide on strategiesA) 1
B)
C)
D)
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24
Find the expected value of the game matrix A = if player 1 and player 2 decide on strategies and Q = .
A)
B)
C)
D)
if player 1 and player 2 decide on strategies and Q = .A)
B)
C)
D)
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25
Find the expected value of the game matrix A = if player 1 and player 2 decide on strategies and Q = .
A)
B)
C)
D)
if player 1 and player 2 decide on strategies and Q = .A)
B)
C)
D)
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26
Solve the matrix game M = indicating optimal strategies and for R and C respectively, and the value v of the game.
A)
B)
C)
D)
indicating optimal strategies and for R and C respectively, and the value v of the game.A)
B)
C)
D)
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27
If a payoff matrix has a row consisting of all 0's, then that row is recessive.
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28
If a matrix game is fair, then both players have optimal strategies that are pure.
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29
In a two-finger Morra game, if player R matches player C, then R wins and if R and C don't match, then C wins. R will win $3 with one finger or two fingers, while C will win $1 with one finger and $5 with 2 fingers. The payoff matrix is Find the optimal strategies and for R and C respectively, and the value v of the game.
A)
B)
C)
D)
Find the optimal strategies and for R and C respectively, and the value v of the game.A)
B)
C)
D)
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30
Two supermarkets, R and C, want to run a promotional on the same item. A market research firm provided the payoff matrix below, where each entry indicates the percentage of customers going to market R at the indicated prices of that item. Find the saddle value, and the optimum strategy for each store.
A) 60%; R sells the item at $1.85, C sells the item at $1.55.
B) 60%; R sells the item at $1.55, C sells the item at $1.85.
C) 50%; R sells the item at $1.85, C sells the item at $1.55.
D) 50%; R sells the item at $1.55, C sells the item at $1.85.
A) 60%; R sells the item at $1.85, C sells the item at $1.55.
B) 60%; R sells the item at $1.55, C sells the item at $1.85.
C) 50%; R sells the item at $1.85, C sells the item at $1.55.
D) 50%; R sells the item at $1.55, C sells the item at $1.85.
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31
QMC decided to put its new product on the market with ads in a trade magazine and a booth at a trade show. It found out that its major competitor ZMC also had decided to advertise the same way for its new product. The payoff matrix shows the increased sales for QMC, as well as decreased sales for ZMC. What is the optimum strategy for QMC and the value of the game?
A) QMC should use ads with probabilityand use booths with probability . The value of the game is .
B) QMC should use ads with probabilityand use booths with probability . The value of the game is .
A) QMC should use ads with probabilityand use booths with probability
. The value of the game is . B) QMC should use ads with probabilityand use booths with probability
. The value of the game is . فتح الحزمة
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32
Two Wally-Worlds are going to build within a three block area. The exact sites will determine the percentage of business above or below 50% each gets, as shown in the payoff matrix. What is the value of the game?
A) 12
B) 6
C) 8
D) 11
A) 12
B) 6
C) 8
D) 11
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33
Two racquetball clubs are in competition in attracting new members. Advertising campaigns are being contemplated by both clubs which emphasize either beginning, intermediate, or advanced player tournaments among members. After careful research, the following results were found:
Thus, if beginner tournaments are featured by both clubs, Club A expects to attract 25% of the new members and Club B expects to attract 75% of the new members, etc. Find the value of the game.
A) 55%
B) 85%
C) 45%
D) 65%
Thus, if beginner tournaments are featured by both clubs, Club A expects to attract 25% of the new members and Club B expects to attract 75% of the new members, etc. Find the value of the game.
A) 55%
B) 85%
C) 45%
D) 65%
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34
The U.S. Marines is playing a war game with side A trying to capture side B's headquarters. Side A has three strategies and side B has four defenses. The payoff matrix shows side A's percentage chance of winning. What is the value of the game?
A) -75
B) -21
C) -41
D) 51
A) -75
B) -21
C) -41
D) 51
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35
Find the smallest integer k ? 0 such that adding k to each entry of the given matrix produces a matrix with all positive payoffs:
-
A) 4
B) 2
C) 1
D) 3
-
A) 4
B) 2
C) 1
D) 3
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36
Find the smallest integer k ? 0 such that adding k to each entry of the given matrix produces a matrix with all positive payoffs:
-
A) 3
B) 2
C) 0
D) 1
-
A) 3
B) 2
C) 0
D) 1
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37
Suppose a matrix game has the following nonstrictly determined matrix:
Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.
A)
B)
Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.
A)
B)
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38
Suppose a matrix game has the following nonstrictly determined matrix:
Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.
A)
B)
Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.
A)
B)
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39
Suppose a matrix game has the following nonstrictly determined matrix:
Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.
A)
B)
Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.
A)
B)
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40
Solve the matrix game using a geometric linear programming approach.
M =
A)
B)
C)
D)
M =
A)
B)
C)
D)
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41
If the value of a matrix game is positive, then all payoffs are positive.
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42
If M is a matrix game, then there is a fair matrix game in which the optimal strategies are those of M.
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43
A small town has two competing grocery stores, store R and store C. Each week each store decides to advertise its specials using either a newspaper advertisement or a mailing. The following payoff matrix indicates the percentage of market gain or loss for each choice of action by store R and store C.
Use linear programming and a geometric approach to find optimal strategies and for store R and store C and the value v of the game.
A)
B)
C)
D)
Use linear programming and a geometric approach to find optimal strategies
and for store R and store C and the value v of the game.A)
B)
C)
D)
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44
Use the simplex method to find the optimum strategy for players A and B and the value of the game for the payoff matrix:
-
A)
B)
C)
D)
-
A)
B)
C)
D)
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45
Use the simplex method to find the optimum strategy for players A and B and the value of the game for the payoff matrix:
-
A)
B)
C)
D)
-
A)
B)
C)
D)
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46
Use the simplex method to find the optimum strategy for players A and B and the value of the game for the payoff matrix:
-
A)
B)
C)
D)
-
A)
B)
C)
D)
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47
Use the simplex method to find the optimum strategy for players A and B and the value of the game for the payoff matrix:
-
A)
B)
C)
D)
-
A)
B)
C)
D)
فتح الحزمة
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48
A company has three different marketing strategies that produce different results depending upon whether inflation is above 6%, between 3% and 6% inclusive, or below 3% annually. The experts cannot predict inflation for the next year. The company has three plans of action and will implement these at varying percentages of its total operation. The payoff matrix for these three plans is given below, with values given in hundred thousands. What is the market strategy for the company that will yield the best expected value?
A) The company should use Plan 1 with probability 4/13, Plan 2 with probability 9/13, and Plan 3 with probability 0.
B) The company should use Plan 1 with probability 5/13, Plan 2 with probability 8/13, and Plan 3 with probability 0.
C) The company should use Plan 1 with probability 1, Plan 2 with probability 0, and Plan 3 with probability 0.
D) The company should use Plan 1 with probability 0, Plan 2 with probability 1, and Plan 3 with probability 0.
A) The company should use Plan 1 with probability 4/13, Plan 2 with probability 9/13, and Plan 3 with probability 0.
B) The company should use Plan 1 with probability 5/13, Plan 2 with probability 8/13, and Plan 3 with probability 0.
C) The company should use Plan 1 with probability 1, Plan 2 with probability 0, and Plan 3 with probability 0.
D) The company should use Plan 1 with probability 0, Plan 2 with probability 1, and Plan 3 with probability 0.
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49
A company has three different marketing strategies that produce different results depending upon whether inflation is above 6%, between 3% and 6% inclusive, or below 3% annually. The experts cannot predict inflation for the next year. The company has three plans of action and will implement these at varying percentages of its total operation. The payoff matrix for these three plans is given below, with values given in hundred thousands. What is the marketing strategy for the company that will yield the best expected value?
A) The company should use Plan 1 with probability 1/3, Plan 2 with probability 1/3, and Plan 3 with probability 1/3.
B) The company should use Plan 1 with probability 0, Plan 2 with probability 1, and Plan 3 with probability 0.
C) The company should use Plan 1 with probability 1, Plan 2 with probability 0, and Plan 3 with probability 0.
D) The company should use Plan 1 with probability 5/13, Plan 2 with probability 0, and Plan 3 with probability 8/13.
A) The company should use Plan 1 with probability 1/3, Plan 2 with probability 1/3, and Plan 3 with probability 1/3.
B) The company should use Plan 1 with probability 0, Plan 2 with probability 1, and Plan 3 with probability 0.
C) The company should use Plan 1 with probability 1, Plan 2 with probability 0, and Plan 3 with probability 0.
D) The company should use Plan 1 with probability 5/13, Plan 2 with probability 0, and Plan 3 with probability 8/13.
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50
A company has three products that fluctuate in favorability. The payoff matrix for the expected profit in tens of thousands of dollars is given below. What are the percentages of each product that the company should make that would maximize the expected value of the profit? Round to the nearest tenth of a percent, if necessary.
A) Product 1: 0%, Product 2: 100%, Product 3: 0%
B) Product 1: 38.5%, Product 2: 0%, Product 3: 61.5%
C) Product 1: 100%, Product 2: 0%, Product 3: 0%
D) Product 1: 33.3%, Product 2: 33.3%, Product 3: 33.3%
A) Product 1: 0%, Product 2: 100%, Product 3: 0%
B) Product 1: 38.5%, Product 2: 0%, Product 3: 61.5%
C) Product 1: 100%, Product 2: 0%, Product 3: 0%
D) Product 1: 33.3%, Product 2: 33.3%, Product 3: 33.3%
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51
A person has hired an investment broker to buy stock. The broker has three different stock funds that are of interest, but each is sensitive to a certain economic indicator that is impossible to predict. The indicator will be positive, neutral, or negative. The table below shows the payoffs in thousands of dollars. Find the strategy that the broker should recommend to maximize the expected value of the investment.
A) Invest in Stock A with probability 1, invest in Stock B with probability 0, and invest in Stock C with probability 0.
B) Invest in Stock A with probability 5/13, invest in Stock B with probability 8/13, and invest in Stock C with probability 0.
C) Invest in Stock A with probability 4/13, invest in Stock B with probability 9/13, and invest in Stock C with probability 0.
D) Invest in Stock A with probability 0, invest in Stock B with probability 1, and invest in Stock C with probability 0.
A) Invest in Stock A with probability 1, invest in Stock B with probability 0, and invest in Stock C with probability 0.
B) Invest in Stock A with probability 5/13, invest in Stock B with probability 8/13, and invest in Stock C with probability 0.
C) Invest in Stock A with probability 4/13, invest in Stock B with probability 9/13, and invest in Stock C with probability 0.
D) Invest in Stock A with probability 0, invest in Stock B with probability 1, and invest in Stock C with probability 0.
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52
A person is considering three different stocks, and each is sensitive to a certain economic indicator. The indicator will be positive, neutral, or negative, and fluctuate randomly. The payoffs are given in the table below, in thousands of dollars. What investment strategy should the person make to obtain the best expected value of profit?
A) Invest in Stock A with probability 1/3, invest in Stock B with probability 1/3, and invest in Stock C with probability 1/3.
B) Invest in Stock A with probability 5/13, invest in Stock B with probability 0, and invest in Stock C with probability 8/13.
C) Invest in Stock A with probability 0, invest in Stock B with probability 1, and invest in Stock C with probability 0.
D) Invest in Stock A with probability 1, invest in Stock B with probability 0, and invest in Stock C with probability 0.
A) Invest in Stock A with probability 1/3, invest in Stock B with probability 1/3, and invest in Stock C with probability 1/3.
B) Invest in Stock A with probability 5/13, invest in Stock B with probability 0, and invest in Stock C with probability 8/13.
C) Invest in Stock A with probability 0, invest in Stock B with probability 1, and invest in Stock C with probability 0.
D) Invest in Stock A with probability 1, invest in Stock B with probability 0, and invest in Stock C with probability 0.
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