Explanation Given Information: The provided payoff matrix is: [ − 4 − 2 − 3 1 − 3 − 2 − 3 1 − 4 ] Formula used: Solve the matrix game as: Step 1: Reduce the provided payoff matrix. Step 2: Make all the entries non negative by addition by a fixed number k and no column should be all zero. Step 3: Write 1s to right of and below the matrix, and solve this primal problem with the help of the simplex method. Step 4: Obtain the optical strategies. Column strategy is enlisted below: 1. Express the solution to the primal problem in the form of column vector . 2. Now, divide each entry of the solution vector by p. 3. Insert zeroes in position corresponding to the columns deleted during reduction. Row strategy is enlisted below: 1. Express the solution to the dual problem in the form of row vector. 2. Now, divide each entry by p . 3. Insert zeroes in position corresponding to the rows deleted during reduction. Value of the game is expressed as, e = 1 p − k Calculation: Consider provided payoff matrix: [ − 4 − 2 − 3 1 − 3 − 2 − 3 1 − 4 ] Add k = 4 to each entry and put 1s to the right and below. The above problem represent by the matrix as, [ 0 2 1 1 5 1 2 1 1 5 0 1 1 1 1 0 ] Obtain the corresponding linear programming problem; Maximize p = x + y + z 2 y + z ≤ 1 5 x + y + 2 z ≤ 1 x + 5 y ≤ 1 Subject to x ≥ 0 , y ≥ 0 , z ≥ 0 . Solve the dual problem using the standard simplex method as: x y z s t u p s 0 2 1 1 0 0 0 1 t 5 1 2 0 1 0 0 1 u 1 5 0 0 0 1 0 1 p − 1 − 1 − 1 0 0 0 1 0 Apply 5 R 3 − R 2 and 5 R 4 + R 2 as, x y z s t u p s 0 2 1 1 0 0 0 1 t 5 1 2 0 1 0 0 1 u 0 24

Finite Mathematics and Application Calculus (Looseleaf) - Text Only

7th Edition

ISBN: 9781337291484

Author: Waner

Publisher: Cengage

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Chapter 6, Problem 26RE

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To calculate: The game matrix when the provided payoff matrix is;

[−4−2−31−3−2−31−4]

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Chapter 6, Problem 25RE

Chapter 6, Problem 27RE

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Chapter 6 Solutions

Finite Mathematics and Application Calculus (Looseleaf) - Text Only

Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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The game matrix when the provided payoff matrix is; [ − 4 − 2 − 3 1 − 3 − 2 − 3 1 − 4 ]

Solution Summary: The author explains the formula used to solve the matrix game as follows: Reduce the provided payoff matrix, make all the entries non negative by addition by a fixed number k, and obtain the optical strategies.

Videos

To calculate: The game matrix when the provided payoff matrix is;

[−4−2−31−3−2−31−4]

Want to see the full answer?

Chapter 6 Solutions

The game matrix when the provided payoff matrix is; [ − 4 − 2 − 3 1 − 3 − 2 − 3 1 − 4 ]

Solution Summary: The author explains the formula used to solve the matrix game as follows: Reduce the provided payoff matrix, make all the entries non negative by addition by a fixed number k, and obtain the optical strategies.

Videos

To calculate: The game matrix when the provided payoff matrix is; [−4−2−31−3−2−31−4]

Want to see the full answer?

Chapter 6 Solutions

To calculate: The game matrix when the provided payoff matrix is;

[−4−2−31−3−2−31−4]