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In this problem we want to understand how the simplex method deals with an LP problem having an infinite number of solutions. Solve: Maximize z = 2.x1 + 4x2 subject to x1 + 2x2 < 5, x1 + x2 < 4, X1, X2 > 0. You will get an optimal solution by doing just one iteration. But there could be more solutions as the objective function has the same slope as the line determined by the second constraint. If you did not know that, what features in the tableau would have signalled this possibility? State your idea as a rule that checks the final tableau to determine if an infinite number of optimal solutions is possible. Give a very brief explanation to justify why your rule should work. Using your rule, do one more iteration to obtain a second optimal solution.

In this problem we want to understand how the simplex method deals with an LP problem having an infinite number of solutions. Solve: Maximize z = 2.x1 + 4x2 subject to x1 + 2x2 < 5, x1 + x2 < 4, X1, X2 > 0. You will get an optimal solution by doing just one iteration. But there could be more solutions as the objective function has the same slope as the line determined by the second constraint. If you did not know that, what features in the tableau would have signalled this possibility? State your idea as a rule that checks the final tableau to determine if an infinite number of optimal solutions is possible. Give a very brief explanation to justify why your rule should work. Using your rule, do one more iteration to obtain a second optimal solution.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.CR: Chapter Review
Problem 70E: A company manufactures two fertilizers, x and y. Each 50-pound bag of fertilizer requires three...
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In this problem we want to understand how the simplex method deals with an LP problem having an infinite number of solutions. Solve: Maximize z = 2.x1 + 4x2 subject to x1 + 2x2 < 5, x1 + x2 < 4, X1, X2 > 0. You will get an optimal solution by doing just one iteration. But there could be more solutions as the objective function has the same slope as the line determined by the second constraint. If you did not know that, what features in the tableau would have signalled this possibility? State your idea as a rule that checks the final tableau to determine if an infinite number of op solutions is possible. Give a very brief explanation to justify why your rule should work. mal Using your rule, do one more iteration to obtain a second optimal solution.
Transcribed Image Text:In this problem we want to understand how the simplex method deals with an LP problem having an infinite number of solutions. Solve: Maximize z = 2.x1 + 4x2 subject to x1 + 2x2 < 5, x1 + x2 < 4, X1, X2 > 0. You will get an optimal solution by doing just one iteration. But there could be more solutions as the objective function has the same slope as the line determined by the second constraint. If you did not know that, what features in the tableau would have signalled this possibility? State your idea as a rule that checks the final tableau to determine if an infinite number of op solutions is possible. Give a very brief explanation to justify why your rule should work. mal Using your rule, do one more iteration to obtain a second optimal solution.
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