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1. Solve the following linear programmne using the 2-phase simplex algorithm. You should give the initial tableau and each further tableau produced during the exe- cution 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. maximize x12x2 x3 - 4x4 subject to 2x1 + x2 - 2x3x4≥ 1, 5x1 + x2 x3x4 ≤ -1, 2x1 + x2 x3 3x4 2, X1, X2, X3, X4 ≥ 0.

1. Solve the following linear programmne using the 2-phase simplex algorithm. You should give the initial tableau and each further tableau produced during the exe- cution 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. maximize x12x2 x3 - 4x4 subject to 2x1 + x2 - 2x3x4≥ 1, 5x1 + x2 x3x4 ≤ -1, 2x1 + x2 x3 3x4 2, X1, X2, X3, X4 ≥ 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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It is generally recommended (here and in the exam) that in your answers, as well as giving the tableaux, you also highlight the appropriate rows and columns and mention the row operations you are carrying out this way, even if your final answer is incorrect, we can easily award you credit for using the right method. 1. Solve the following linear programmne using the 2-phase simplex algorithm. You should give the initial tableau and each further tableau produced during the exe- cution 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. maximize x12x2 x3 - 4x4 subject to 2x1 + x22x3x4 ≥ 1, 5x1 + x2 x3 x4 ≤ −1, 2x1 x2 x3 3x4 2, X1, X2, X3, X4≥ 0. 2. Apply the first phase of the 2-phase simplex algorithm to the following linear pro- gramme giving the initial tableau and each further tableau produced. Give the starting tableau for the second phase if there is one. 2x1 + x2+3x3 maximize subject to x2 x32, x13x22x3 ≥ 3, 2x12x2 x3 = 4, x1, x2, x3 0.
Transcribed Image Text:It is generally recommended (here and in the exam) that in your answers, as well as giving the tableaux, you also highlight the appropriate rows and columns and mention the row operations you are carrying out this way, even if your final answer is incorrect, we can easily award you credit for using the right method. 1. Solve the following linear programmne using the 2-phase simplex algorithm. You should give the initial tableau and each further tableau produced during the exe- cution 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. maximize x12x2 x3 - 4x4 subject to 2x1 + x22x3x4 ≥ 1, 5x1 + x2 x3 x4 ≤ −1, 2x1 x2 x3 3x4 2, X1, X2, X3, X4≥ 0. 2. Apply the first phase of the 2-phase simplex algorithm to the following linear pro- gramme giving the initial tableau and each further tableau produced. Give the starting tableau for the second phase if there is one. 2x1 + x2+3x3 maximize subject to x2 x32, x13x22x3 ≥ 3, 2x12x2 x3 = 4, x1, x2, x3 0.
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