Explanation Procedure used: First convert the system into a matrix equation of the form A X = B , and then use X = A − 1 B to obtain X . Calculation: Given that, each executive receives as a bonus a percentage of the portion of the annual profit that remains after the bonus has been deducted. Also the annual profit is $2 million. Let x 1 denote the president’s bonus, x 2 denote the executive vice president’s bonus, x 3 denote the associate vice president’s bonus , x 4 denote the assistant vice president’s bonus and x 5 denote the sales manager’s bonus. Express the given information using mathematical model as, x 1 + 0.03 x 2 + 0.03 x 3 + 0.03 x 4 + 0.03 x 5 = 60000 0.25 x 1 + x 2 + 0.25 x 3 + 0.25 x 4 + 0.25 x 5 = 50000 0.02 x 1 + 0.02 x 2 + x 3 + 0.02 x 4 + 0.02 x 5 = 40000 0.015 x 1 + 0.015 x 2 + 0.015 x 3 + 0.015 x 4 + 0.015 x 5 = 30000 0.01 x 1 + 0.01 x 2 + 0.01 x 3 + x 4 + 0.01 x 5 = 20000 The corresponding matrix equation A X = B for the given system of equations is, [ 10.03 0.03 0.03 0.03 0.03 0.025 1 0.025 0.025 0.025 0.02 0.02 1 0.02 0.02 0.015 0.015 0.015 1 0.015 0.01 0.01 0.01 0.01 1 ] [ x 1 x 2 x 3 x 4 x 5 ] = [ 60000 50000 40000 30000 20000 ] Thus, the coefficient matrix is A = [ 10.03 0.03 0.03 0.03 0.03 0.025 1 0.025 0.025 0.025 0.02 0.02 1 0.02 0.02 0.015 0.015 0.015 1 0.015 0.01 0.01 0.01 0.01 1 ] . Obtain the inverse of the coefficient matrix as follows. Form the augmented matrix [ A I ] in order to obtain the inverse of the matrix. [ 1 0.03 0.03 0.03 0.03 1 0 0 0 0 0.025 1 0.025 0.025 0.025 0 1 0 0 0 0.02 0.02 1 0.02 0.02 0 0 1 0 0 0.015 0.015 0.015 1 0.015 0 0 0 1 0 0

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134674148

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

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Chapter 4.6, Problem 68E

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The bonus for each executive.

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Chapter 4.6, Problem 67E

Chapter 4.6, Problem 69E

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Chapter 4 Solutions

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 4.1 - Solve by graphing and check: 2x − y = −3 x + 2y =...Ch. 4.1 - Solve each of the following systems by graphing: x...Ch. 4.1 - Prob. 3MP Ch. 4.1 - Prob. 4MP Ch. 4.1 - Prob. 5MP Ch. 4.1 - Prob. 6MP Ch. 4.1 - Prob. 7MP Ch. 4.1 - Prob. 1ED Ch. 4.1 - Prob. 2ED Ch. 4.1 - In Problems 1–6, find the x and y coordinates of...

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