Explanation There are two linear inequalities.Add the slack variable to each constraint and write the linear equation as maximize z = 5 x 1 + 2 x 2 with respect to equations, 2 x 1 + 4 x 2 + s 1 = 15 3 x 1 + x 2 + s 2 = 10 with x 1 ≥ 0 , x 2 ≥ 0 , s 1 ≥ 0 , s 2 ≥ 0 Hence, rewrite the objective function as − 5 x 1 − 2 x 2 + z = 0 From the above, the initial table is obtained as [ x 1 x 2 s 1 s 2 z 2 4 1 0 0 15 3 1 0 1 0 10 − 5 − 2 0 0 1 0 ] _ The numbers in the bottom row, which are the initial functions, are called indicators. So, take pivot element from the above table. Therefore, the most negative indicator is − 5 in x 1 column. Then the pivot produces the new table, leading to another system of equations; this was obtained from original problem. Hence, we need to find the quotients, which can be calculated as follows: For column x 1 , the quotient can be calculated as 15 2 = 7.5 10 3 ≈ 3.3 Here, 3.3 is the smallest quotient. So, pivot element is 3 in the first column and second row. So that we get [ x 1 x 2 s 1 s 2 z 2 4 1 0 0 15 3 1 0 1 0 10 − 5 − 2 0 0 1 0 ] _ We need to perform the row transformation as − 2 R 2 + 3 R 1 → R 1 5 R 2 + 3 R 3 → R 3 So [ x 1 x 2 s 1 s 2 z 0 10 3 − 2 0 25 3 1 0 1 0 10 0 − 1 0 5 3 50 ] _ Again, we are having negative indicator and we need to repeat the same process and here we have only one negative. From that, take the most negative indicator, that is,−1. From the quotients can be calculated as 25 10 = 2.5 and 10 1 = 10 . Here 2.5 is the smallest quotient and the pivot element is 10 in the second column and first row

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 4 Solutions

Finite Mathematics (11th Edition)

Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 2E Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 4E Ch. 4.1 - For Exercises 5-8. (a) determine the number of...Ch. 4.1 - Prob. 6E Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - Introduce slack variables as necessary, then...Ch. 4.1 - Introduce slack variables as necessary, then write...

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