Explanation Given: The given conditions are, x + y ≤ 80 3 x ≤ 90 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 have not been reached. Calculation: Consider the given equations. P = 5 x + 3 y Introduce the slack variables, u , v and rewrite the objective function in the standard form that gives the system of linear equation as follows, x + y + u = 80 3 x + v = 5 − 5 x − 3 y + P = 0 The initial simplex tableau is as follows, x y u v P Constant 1 1 1 0 0 80 3 0 0 1 0 90 − 5 − 3 0 0 1 0 Some of the elements in the last row are negative, so it is not in final form. Select the pivot row, pivot element and column for further simplification. Apply the row operation R 2 → 1 3 R 2 . x y u v P Constant Ratio 1 1 1 0 0 80 80 1 = 80 1 0 0 1 0 30 90 3 = 30 − 5 − 3 0 0 1 0 Apply the row operation R 2 → R 2 − R 1 and R 3 → R 3 + 5 R 1

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ISBN: 9780357308615

Author: Tan

Publisher: CENGAGE L

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Chapter 4.1, Problem 18E

To determine

To maximize:

The objective functions P=5x+3y by the simplex method.

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Chapter 4.1, Problem 17E

Chapter 4.1, Problem 19E

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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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