Explanation Given: The linear equation maximize z = x 1 + x 2 + 4 x 3 + 5 x 4 . Subject to x 1 + 2 x 2 + 3 x 3 + x 4 ≤ 115 2 x 1 + x 2 + 8 x 3 + 5 x 4 ≤ 200 x 1 + x 3 ≤ 50 with x 1 ≥ 0 , x 2 ≥ 0 , x 3 ≥ 0 , x 4 ≥ 0 . Explanation: Here there are threelinear inequalities.Add slack variables to each constraint and writethe linear equation as Maximize z = x 1 + x 2 + 4 x 3 + 5 x 4 . So x 1 + 2 x 2 + 3 x 3 + x 4 + s 1 = 115 2 x 1 + x 2 + 8 x 3 + 5 x 4 + s 2 = 200 x 1 + x 3 + s 3 = 50 Hence, rewrite the objective function as − x 1 − x 2 − 4 x 3 − 5 x 4 + z = 0 From the above, the initial table is obtained as [ x 1 x 2 x 3 x 4 s 1 s 2 s 3 z 1 2 3 1 1 0 0 0 115 2 1 8 5 0 1 0 0 200 1 0 1 0 0 0 1 0 50 − 1 − 1 − 4 − 5 0 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 4 column. Then, the pivot produces the new tableau, 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 4 , the quotient can be calculated as 115 1 = 115 200 5 = 40 50 0 is not defined Here, 40 is the smallest quotient. So, pivot element is 5 in the fourth column and second row

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

11th Edition

ISBN: 9780133886818

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

Publisher: PEARSON

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Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (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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