Solve each of the following linear programs 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. Ideally you should indicate the highlighted row and columns in each pivot step as well as the row operations you carry out. This is in order to gain credit even if the final answer is incorrect. 2. maximize 2x₁ +4x₂ - 3 subject to -2x1 + x3 ≤ 3, 1x₁2x₂ + 4x3 ≤ 2, 1 + x₂-3x3 ≤ 2, 2x₁x₂ + x32-6, I1, I2, I3 20

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Chapter6: Linear Systems
Section6.8: Linear Programming
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Solve each of the following linear programs 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.
Ideally you should indicate the highlighted row and columns in each pivot step as well
as the row operations you carry out. This is in order to gain credit even if the final answer
is incorrect.
2.
maximize 2x₁ +4x₂ - 3
subject to
-2x1 + x3 ≤ 3,
1x₁2x₂ + 4x3 ≤ 2,
1 + x₂-3x3 ≤ 2,
2x₁x₂ + x32-6,
I1, I2, I3 20
Transcribed Image Text:Solve each of the following linear programs 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. Ideally you should indicate the highlighted row and columns in each pivot step as well as the row operations you carry out. This is in order to gain credit even if the final answer is incorrect. 2. maximize 2x₁ +4x₂ - 3 subject to -2x1 + x3 ≤ 3, 1x₁2x₂ + 4x3 ≤ 2, 1 + x₂-3x3 ≤ 2, 2x₁x₂ + x32-6, I1, I2, I3 20
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