Explanation Procedure used: Gauss-Jordan Elimination: Step 1: Choose the leftmost nonzero column and use appropriate row operations to get a 1 at the top. Step 2: Use multiples of the row containing the 1 from step 1 to get zeroes in all remaining places in the column containing this 1. Step 3: Repeat step 1 with the submatrix formed by (mentally) deleting the row used in step 2 and all rows above this row. Step 4: Repeat step 2 with the entire matrix, including the rows deleted mentally. Continue this process until the entire matrix is in reduced form. Calculation: Obtain the tax liability of the corporation when the state and local tax are not deduced as follows. Given that, the total taxable income of the corporation is 7 , 650 , 000 . Also the federal income tax rate, state tax rate and the local tax rate is given as, 50 % , 20 % and 10 % respectively. Define the following variables for each type tax rates. x 1 = federal income tax x 2 = state income tax x 3 = local income tax The mathematical model for the problem with the given data can be formulated as follows. x 1 + 0.5 x 2 + 0 x 3 = 3 , 825 , 000 0.2 x 1 + x 2 + 0 x 3 = 1 , 530 , 000 0.1 x 1 + 0.1 x 2 + x 3 = 765 , 000 This forms a system of linear equations. Solve this system of linear equations by Gauss-Jordan elimination method as follows. The augmented matrix is, [ 1 0.5 0 3 , 825 , 000 0.2 1 0 1 , 530 , 000 0.1 0.1 1 765 , 000 ] Perform the below row operations to reduce the matrix. Pivot element is found in the first row. So perform the row operations to eliminate the first row [ 1 0.5 0 3 , 825 , 000 0.2 1 0 1 , 530 , 000 0.1 0.1 1 765 , 000 ] ∼ [ 1 0.5 0 3 , 825 , 000 0 0.9 0 765 , 000 0 0.05 1 382 , 500 ] R 2 − 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 4.3, Problem 80E

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The tax liability of the corporation when the state and local tax deductions are not considered.

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Chapter 4.3, Problem 79E

Chapter 4.3, Problem 81E

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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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