Explanation Given Information: The provided payoff matrix is: [ − 3 0 1 − 4 0 0 0 − 1 − 2 ] 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 1 s to the 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 zeros 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 zeros in positions corresponding to the rows deleted during reduction. Value of the game is expressed as, e = 1 p − k Calculation: Consider the provided payoff matrix is: [ − 3 0 1 − 4 0 0 0 − 1 − 2 ] Add k = 3 to each entry and put 1 s to the right and be below. Represent this above problem by the matrix as, [ 0 3 4 3 2 1 1 1 1 1 1 0 ] Obtain the corresponding linear programming problem as, Maximize p = x + y + z Subjuect to 3 y + 4 z ≤ 1 3 x + 2 y + z ≤ 1 x ≥ 0 , y ≥ 0

Finite Mathematics and Application Calculus (Looseleaf) - Text Only

7th Edition

ISBN: 9781337291484

Author: Waner

Publisher: Cengage

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Chapter 6, Problem 24RE

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

[−301−4000−1−2].

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Chapter 6, Problem 23RE

Chapter 6, Problem 25RE

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Finite Mathematics and Application Calculus (Looseleaf) - Text Only

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The game matrix when the provided payoff matrix is [ − 3 0 1 − 4 0 0 0 − 1 − 2 ] .

Solution Summary: The author explains how to solve the matrix game using the simplex method.

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

[−301−4000−1−2].

Want to see the full answer?

Chapter 6 Solutions

The game matrix when the provided payoff matrix is [ − 3 0 1 − 4 0 0 0 − 1 − 2 ] .

Solution Summary: The author explains how to solve the matrix game using the simplex method.

Videos

To calculate: The game matrix when the provided payoff matrix is [−301−4000−1−2].

Want to see the full answer?

Chapter 6 Solutions

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

[−301−4000−1−2].