Explanation Given: The given problem is, Minimize C = 2 x − 3 y + 4 z subject to − x + 2 y − z ≤ 8 x − 2 y + 2 z ≤ 10 2 x + 4 y − 3 z ≤ 12 x ≥ 0 , y ≥ 0 , z ≥ 0 Approach: 1. In the standard maximization problem the objective function is to be maximized. 2. All variables involved in the problem should be non-negative. 3. Each linear constraint may be written so that the expression involving the variables is less than or equal to a non-negative constraint. 4. The optimal solution is reached when all the entries of bottom row of the simplex tableau are non-negative. Calculation: Consider the given linear programming problem. Rewrite the problem as maximization problem with P = − C . Maximize P = − 2 x + 3 y − 4 z subject to − x + 2 y − z ≤ 8 x − 2 y + 2 z ≤ 10 2 x + 4 y − 3 z ≤ 12 x ≥ 0 , y ≥ 0 , z ≥ 0 Introduce the slack variables u v and w in the given linear programming problem, − x + 2 y − z + u = 8 x − 2 y + 2 z + v = 10 2 x + 4 y − 3 z + w = 12 2 x − 3 y + 4 z + P = 0 The initial simplex tableau is, x y z u v w P Constant − 1 2 − 1 1 0 0 0 8 1 − 2

WebAssign Printed Access Card for Tan's Finite Mathematics for the Managerial, Life, and Social Sciences, 12th Edition, Single-Term

12th Edition

ISBN: 9781337652766

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 4.3, Problem 15E

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To solve:

The given linear programming problem.

Minimize C=2x−3y+4z

subject to −x+2y−z≤8 x−2y+2z≤10 2x+4y−3z≤12 x≥0,y≥0,z≥0

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Chapter 4.3, Problem 14E

Chapter 4.3, Problem 16E

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Chapter 4 Solutions

WebAssign Printed Access Card for Tan's Finite Mathematics for the Managerial, Life, and Social Sciences, 12th Edition, Single-Term

Ch. 4.1 - Give the three characteristics of a standard...Ch. 4.1 - a. When the initial simplex tableau is set up, how...Ch. 4.1 - In the simplex method, how is a pivoted column...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7-16, determine whether the given...

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The given linear programming problem. Minimize C = 2 x − 3 y + 4 z subject to − x + 2 y − z ≤ 8 x − 2 y + 2 z ≤ 10 2 x + 4 y − 3 z ≤ 12 x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author explains the optimal solution for the linear programming problem.

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To solve:

The given linear programming problem.

Minimize C=2x−3y+4z

subject to −x+2y−z≤8 x−2y+2z≤10 2x+4y−3z≤12 x≥0,y≥0,z≥0

Want to see the full answer?

Chapter 4 Solutions

The given linear programming problem. Minimize C = 2 x − 3 y + 4 z subject to − x + 2 y − z ≤ 8 x − 2 y + 2 z ≤ 10 2 x + 4 y − 3 z ≤ 12 x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author explains the optimal solution for the linear programming problem.

Videos

To solve: The given linear programming problem. Minimize C=2x−3y+4z subject to −x+2y−z≤8 x−2y+2z≤10 2x+4y−3z≤12 x≥0,y≥0,z≥0

Want to see the full answer?

Chapter 4 Solutions

To solve:

The given linear programming problem.

Minimize C=2x−3y+4z

subject to −x+2y−z≤8 x−2y+2z≤10 2x+4y−3z≤12 x≥0,y≥0,z≥0