# Questions tagged [two-phase-simplex]

For questions about the two phase simplex method, which is an algorithm to solve a linear program which has no initial basic feasible solution.

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### Generating random linear programming problems

I've just finished writing a a linear programming problem solver which uses the simplex method. Now I would like to start optimizing my solver but before I can do this, I need a way of reliably ...
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### Forbidden range for a linear programming variable

I would like to express a linear program having a variable that can only be greater or equal than a constant $c$ or equal to $0$. The range $]0; c[$ being unallowed. Do you know a way to express this ...
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### Expressing problems in canonical form for solving with simplex

The Picnic Hamper Company has a store containing 10,000kg of nuts, 4000 packs of smoked salmon, 2000 bottles of wine and 1500 Victoria sponges. It intends to use these goods to make up three different ...
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### Two phase method in linear programming

Suppose following tableau came after one iteration in first phase of a two phase method problem, here $s_1$ is a surplus variable and $s_2$ is a slack variable $w$ is a artificial variable. I tried ...
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### Two-phase simplex

The upper part of the image attached is the question and lower part is the solution. I did the exact same table as table4 in the picture, yet I put the ratio of  as 0.5/0.5=1 instead. Could someone ...
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### Is simplex method weaker than other methods?

Given linear program: $$\text{min } x_1 - x_2 + 2 x_3$$ s.t.: $$-3x_1 + x_2 + x_3 = 4$$ $$x_1 - x_2 + x_3 = 3$$ $$x_i \geq 0; i = \{1,2,3\}$$ solution by simplex method (with double pass) is ...
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### Linear Program Transformations

I have a Linear Program with constrains of the form: $$a_{11}x_1+a_{12}x_2+\ldots\le 0$$ $$a_{21}x_1+a_{22}x_2+\ldots\le 0$$ $$a_{31}x_1+a_{32}x_2+\ldots\le 0$$ My problem is that if I try to ...
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### How does the two phase method for linear programs work…

I understand that by adding artificial variables the problem can be reformulated as a new problem where the "starting point" is readily found. What I don't get is how when this extended problem is ...
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### General solution to linear program?

Source of the Problem The problem comes from an application in economics concerning trade between agents to maximize aggregate "wealth". More exactly, there are $m$ agents and $n$ groups and we ...
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### Simplex Algorithm (Two-Phase) - Finding pivot entries consistent with the simplex method

I'm working through the examples in my professor's class notes, but I can't figure out how to solve this problem: Example: In the following standard tableau, mark by * the choices for the pivot ...
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### List the six possible bases of the LP P and find their corresponding solutions

Consider the following LP P: max z = 22x_1 - 12x_2 subject to: 8x_1 + 4x_2 \le 15 2x_1 + 6x_2 \le 7 x_1, x_2 \ge 0 ...
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### Proof verification for simplex method problems

I was studying simplex method in LPP from "Introduction to Linear Optimization by Bertsimas and Tsitsiklis", and came across this problem: Consider the simplex method applied to a standard form ...
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### calculating the extreme rays of a polyhedra

How could I go about the problem finding the extreme rays of a polyhedral defined by constraints $x_1-x_2 \geq -2$ $x_1+x_2 \geq 1$ $x_1,x_2 \geq 0$ I know for certain that given a max or min ...
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### In Simplex Method, can I move from a basic solution $x^{*}$ to the other $y^{*}$ by pivoting zero cost in Tableau?

Suppose that $B_1$ is the bases for $x^{*}$ and I want to go to the second solution $y^{*}$ with bases $B_2$, how to go to the second optimal solution through pivoting? My attempt was trying to prove ...
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### Operations Research: Simplex Table Unbound Optimal Solution

The problem statement, all variables and given/known data Hi I am looking at this quesiton attached part c). Relevant equations The attempt at a solution I can by my notes which tell me that if I ...
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### Complexity of the first phase method

(first post on math SE) I am looking for a formal upper-bound on the number of iterations in the first phase, in terms of the number of artificial variables (A.V). I have some intuition that it ...
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### Show that it as no feasible solution.

An optimization problem: $$\text{ maximize } z=8x+6y$$ $$\text{ such that: } x-y ≤ 0.6 \text{ and } x-y≥2$$ Show that it as no feasible solution using SIMPLEX METHOD. It seems very logical that ...
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### Maximising a Linear Programming Problem

Maximize $w=2x+3y+6z$ subject to $2x+y+z \le 5$ $3y+2z \le 6$ $x,y,z \ge 0$ Is the optimal solution unique? Justify your answer. I tried to solve it by Simplex method. In the second iteration, ...
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### How to Adequately Implement Phase I of Two-Phase Simplex Algorithm on a Computer with Floating Point Error

I'm currently trying to write some code that implements Phase I of the two-phase Simplex Algorithm described here: http://www.statslab.cam.ac.uk/~ff271/teaching/opt/notes/notes8.pdf In order to test ...
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### Simplex method state after first phase

I'm implementing a simplex method solver for a standard problem  \begin{aligned} \operatorname{minimize} \qquad&c^T x\\ \operatorname{subjected to} \qquad&Ax = b\\ &x \geq 0\\ \end{...
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### If we start with a feasible tableau in simplex method, are we basically generating a different feasible point in every pivot step?

This is a true and false question. The actual question reads: "In solving a linear program by the simplex method, starting with a feasible tableau, a different feasible point is generated after every ...
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### Simplex method and basic solutions

I have put this into the form $0.5x_1 + 0.25x_2 + x_3=6$ $-x_1 - 3x_2 + x_4=-2$ $x_1 + x_2 = 10$ Is this correct? If so, how do I find a basic solution so that I can begin the simplex algorithm?