Explanation Given: The objective function to be maximized is P = 5 x + 2 y . The constraints are, 4 x + 3 y ≤ 30 2 x − 3 y ≤ 6 x ≥ 0 , y ≥ 0 Approach: (1) If all the entries are nonnegative, the optimal solution has been reached. (2) If there is one or more negative entries, the optimal solution has not been reached. Calculation: Introduce the slack variables, u , and v in the given conditions and rewrite the objective function in the standard form that gives the system of linear equation as follows, 4 x + 3 y + u = 30 2 x − 3 y + v = 6 P − 5 x − 2 y = 0 Construct the initial simplex table. x y u v P Constant 4 3 1 0 0 30 2 − 3 0 1 0 6 − 5 − 2 0 0 1 0 All the element in the last row are not non negative. So, the above simplex table is not in its final form. Calculate the pivot element. The most negative element in the last row is ( − 5 ) that lies in column 1 . So, the pivot column is column 1. Calculate the pivot row. x y u v P Constant Ratio 4 3 1 0 0 30 30 4 = 7.5 2 − 3 0 1 0 6 6 2 = 3 − 5 − 2 0 0 1 0 The least ratio is 3 that lies in row 2 . So the pivot row is the second row. So, the element corresponding to pivot column and the pivot row is 2 . Apply the row operation R 2 → 1 2 R 2 in the above table. x y u v P Constant 4 3 1 0 0 30 1 − 3 2 0 1 2 0 3 − 5 − 2 0 0 1 0 Apply operation R 1 → R 1 − 4 R 2 and R 3 → R 3 + 5 R 2 . x y u v P Constant 0 9 1 − 2 0 18 1 − 3 2 0 1 2 0 3 0 − 19 2 0 2

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

11th Edition

ISBN: 9781285464657

Author: Soo T. Tan

Publisher: Brooks Cole

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Chapter 4.BMO, Problem 3BMO

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To find:

The solution of the linear programming problem using Simplex method.

Maximize
Subject to P=5x+2y
4x+3y≤302x−3y≤6x≥0,y≥0

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Chapter 4.BMO, Problem 2BMO

Chapter 4.BMO, Problem 4BMO

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Chapter 4 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

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 solution of the linear programming problem using Simplex method. Maximize Subject to P = 5 x + 2 y 4 x + 3 y ≤ 30 2 x − 3 y ≤ 6 x ≥ 0 , y ≥ 0

Solution Summary: The author explains the solution of the linear programming problem using Simplex method.

Videos

To find:

The solution of the linear programming problem using Simplex method.

Maximize
Subject to P=5x+2y
4x+3y≤302x−3y≤6x≥0,y≥0

Want to see the full answer?

Chapter 4 Solutions

The solution of the linear programming problem using Simplex method. Maximize Subject to P = 5 x + 2 y 4 x + 3 y ≤ 30 2 x − 3 y ≤ 6 x ≥ 0 , y ≥ 0

Solution Summary: The author explains the solution of the linear programming problem using Simplex method.

Videos

To find: The solution of the linear programming problem using Simplex method. MaximizeSubject to P=5x+2y4x+3y≤302x−3y≤6x≥0,y≥0

Want to see the full answer?

Chapter 4 Solutions

To find:

The solution of the linear programming problem using Simplex method.

Maximize
Subject to P=5x+2y
4x+3y≤302x−3y≤6x≥0,y≥0