Explanation Given: Maximize z = 2 x 1 + 5 x 2 + x 3 Subject to: x 1 − 5 x 2 + 2 x 3 ≤ 30 4 x 1 − 3 x 2 + 6 x 3 ≤ 72 with x 1 ≥ 0 , x 2 ≥ 0 and x 3 ≥ 0 Explanation: Step 1: Add slack variables or basic variables to each constraint to convert it into linear equations. Basic variables are the variables that are nonzero. As a result x 1 − 5 x 2 + 2 x 3 + s 1 = 30 4 x 1 − 3 x 2 + 6 x 3 + s 2 = 72 with x 1 ≥ 0 , x 2 ≥ 0 , x 3 ≥ 0 and s 1 , s 2 ≥ 0 Here, s 1 , s 2 are basic variables and x 1 , x 2 , x 3 are nonbasic variables. Rewrite objective function: z − 2 x 1 − 5 x 2 − x 3 = 0 Step 2: Represent the system of linear equations obtained above in simplex tableau. This is the initial tableau. [ x 1 x 2 x 3 s 1 s 2 z s 1 1 − 5 2 1 0 0 30 s 2

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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Chapter 4.2, Problem 16E

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Chapter 4 Solutions

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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