Explanation Given: The minimization function is: w = y 1 + 2 y 2 + 6 y 3 Subjected to the system of inequality or constraints: 3 y 1 + 4 y 2 + 6 y 3 ≥ 8 y 1 + 5 y 2 + 2 y 3 ≥ 12 Where, y ≥ 0 , y 2 ≥ 0 , y 3 ≥ 0 Calculation: First, find the dual problem with maximization. Find the argument matrix with a system of inequality and the coefficient of the objective function. But the negative sign is not considered then, 3 4 6 8 1 5 2 12 1 2 6 0 The above argument matrix contains first two-rows show coefficients of constraints and the last row shows the coefficient of the objective function. Now, find the transpose matrix of the argument matrix to find the dual problem. 3 1 1 4 5 2 6 2 6 8 12 0 Now, use ( x ) instead of ( y ) for dual problem, and the above transpose matrix shows that the first two rows as constraints and the last row are an objective function. Then, The maximization function is, z = 8 x 1 + 12 x 2 And, inequalities are, 3 x 1 + x 2 ≤ 1 4 x 1 + 4 x 2 ≤ 2 6 x 1 + 2 x 2 ≤ 6 x 1 ≥ 0 , x 2 ≥ 0 Now, use simplex method to solve the maximization problem. The maximization function is: z = 8 x 1 + 12 x 2 Subjected to constrains or system of inequality, 3 x 1 + x 2 ≤ 1 4 x 1 + 4 x 2 ≤ 2 6 x 1 + 2 x 2 ≤ 6 x 1 ≥ 0 , x 2 ≥ 0 Now, use slack variables for converting the inequalities into equalities equations, then the equations are, 3 x 1 + x 2 + s 1 = 1 4 x 1 + 4 x 2 + s 2 = 2 6 x 1 + 2 x 2 + s 3 = 6 Form the simplex table, x 1 x 2 s 1 s 2 s 3 3 1 1 0 0 1 4 4 0 1 0 2 6 2 0 0 1 6 − 8 − 12 0 0 0 0 The last row of the above table shows the coefficient of the objective function and the row-1, row-2, and row-3 show the coefficient of the constraints. Now, find the pivot column and pivot row of the table

MyLab Math with Pearson eText -- Standalone Access Card -- for Mathematics with Applications in the Management, Natural, and Social Sciences (12th Edition)

12th Edition

ISBN: 9780134856551

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 7.6, Problem 14E

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To calculate: The minimum value of the function and the point at which the value of the function is minimum by using duality theorem.

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Chapter 7.6, Problem 13E

Chapter 7.6, Problem 15E

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MyLab Math with Pearson eText -- Standalone Access Card -- for Mathematics with Applications in the Management, Natural, and Social Sciences (12th Edition)

Ch. 7.1 - Checkpoint 1 Graph the given...Ch. 7.1 - Prob. 2CP Ch. 7.1 - Prob. 3CP Ch. 7.1 - Prob. 4CP Ch. 7.1 - Prob. 5CP Ch. 7.1 - Checkpoint 6 Graph the feasible region of the...Ch. 7.1 - Prob. 7CP Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...

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