Explanation Given Information: The provided nonlinear programming problem is: Maximize p = x y subject to x ≥ 0 , y ≥ 0 , x + y ≤ 2 . Formula Used: Solving A Matrix Game: Step1: Reduce the payoff matrix by dominance. Step2: Add a fixed number k to each of the entries so that they all become nonnegative and no column is zero. Step3: Write 1s to the right and below the matrix, and then write down the associated standard maximization problem. Solve this primal problem using the simplex method. Step4: Find the optimal strategies and the expected value. Calculation: Consider the provided payoff matrix: P = [ − 3 − 2 3 1 0 0 − 2 2 1 ] Firstly, add k = 3 to each entry so that every entry remains positive: P = [ 0 1 6 4 3 3 1 5 4 ] Introduce 1s to the right and below as: P = [ 0 1 6 1 4 3 3 1 1 5 4 1 1 1 1 0 ] Now, the LP problem is given as: Maximize p = x + y + z subject to y + 6 z ≤ 1 , 4 x + 3 y + 3 z ≤ 1 , x + 5 y + 4 z ≤ 1 , x ≥ 0 , y ≥ 0 , z ≥ 0 . Apply the Simplex method to solve the problem. The tableaux are constructed as: x y z s t u p s 0 1 6 1 0 0 0 1 t 4 3 3 0 1 0 0 1 u 1 5 4 0 0 1 0 1 p − 1 − 1 − 1 0 0 0 1 0 The pivot column is the column that leads with the 1s in the rows. Here the first column is the pivot column. To convert the 1 in the first column to zero, perform the operation 4 R 3 − R 2 in R 3 and 4 R 4 + R 2 in R 4 to obtain the further tableaux as, x y z s t u p s 0 1 6 1 0 0 0 1 t 4 3 3 0 1 0 0 1 u 0 17 13 0 − 1 4 0 3 p 0 − 1 − 1 0 1 0 4 1 Similarly, perform the operation 17 R 1 − R 3 in R 1 , 17

Bundle: Finite Mathematics, 7th + WebAssign Printed Access Card for Waner/Costenoble's Finite Mathematics, 7th Edition, Single-Term

7th Edition

ISBN: 9781337604956

Author: Waner

Publisher: CENGAGE L

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Chapter 5, Problem 25RE

To determine

To calculate: The solution with the given payoff matrix:

P=[−3−23100−221]

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Chapter 5, Problem 24RE

Chapter 5, Problem 26RE

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Bundle: Finite Mathematics, 7th + WebAssign Printed Access Card for Waner/Costenoble's Finite Mathematics, 7th Edition, Single-Term

Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 6E Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 9E Ch. 5.1 - In Exercises 1-26, sketch the region that...

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