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Solve the following linear program using the simplex algorithm. You should give the initial tableau and each further tableau produced during the execution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. You should indicate the highlighted row and columns in each pivot step as well as the row operations you carry out. 1. maximize 2x13x25x3 + x4 subject to x1+x22x3 + x4 ≤ 2, 3x23x33x4 ≤ 6, 3x12x22x3 + x4 ≤7, X1, X2, X3, X4 ≥ 0 2. Suppose that we are carrying out the simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? X2 X3 S1 S2 S3 S4 x1 S1 -2 0 1 1 0 0 0 3 S2 3 0 -2 0 1 2 0 6 x2 1 1 -3 0 0 1 0 2 S4 -3 0 2 0 0 -2 -20 11 −1 1 4 00-40-8

Solve the following linear program using the simplex algorithm. You should give the initial tableau and each further tableau produced during the execution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. You should indicate the highlighted row and columns in each pivot step as well as the row operations you carry out. 1. maximize 2x13x25x3 + x4 subject to x1+x22x3 + x4 ≤ 2, 3x23x33x4 ≤ 6, 3x12x22x3 + x4 ≤7, X1, X2, X3, X4 ≥ 0 2. Suppose that we are carrying out the simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? X2 X3 S1 S2 S3 S4 x1 S1 -2 0 1 1 0 0 0 3 S2 3 0 -2 0 1 2 0 6 x2 1 1 -3 0 0 1 0 2 S4 -3 0 2 0 0 -2 -20 11 −1 1 4 00-40-8

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.4: Applications Of Eigenvalues And Eigenvectors
Problem 69E: Use your schools library, the Internet, or some other reference source to find the real-life...
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Solve the following linear program using the simplex algorithm. You should give the initial tableau and each further tableau produced during the execution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. You should indicate the highlighted row and columns in each pivot step as well as the row operations you carry out. 1. maximize 2x13x25x3 + x4 subject to x1+x22x3 + x4 ≤ 2, 3x23x33x4 ≤ 6, 3x12x22x3 + x4 ≤7, X1, X2, X3, X4 ≥ 0 2. Suppose that we are carrying out the simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? X2 X3 S1 S2 S3 S4 x1 S1 -2 0 1 1 0 0 0 3 S2 3 0 -2 0 1 2 0 6 x2 1 1 -3 0 0 1 0 2 S4 -3 0 2 0 0 -2 -20 11 −1 1 4 00-40-8
Transcribed Image Text:Solve the following linear program using the simplex algorithm. You should give the initial tableau and each further tableau produced during the execution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. You should indicate the highlighted row and columns in each pivot step as well as the row operations you carry out. 1. maximize 2x13x25x3 + x4 subject to x1+x22x3 + x4 ≤ 2, 3x23x33x4 ≤ 6, 3x12x22x3 + x4 ≤7, X1, X2, X3, X4 ≥ 0 2. Suppose that we are carrying out the simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? X2 X3 S1 S2 S3 S4 x1 S1 -2 0 1 1 0 0 0 3 S2 3 0 -2 0 1 2 0 6 x2 1 1 -3 0 0 1 0 2 S4 -3 0 2 0 0 -2 -20 11 −1 1 4 00-40-8
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