# 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.

28 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
139 views

303 views

### 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 ...
148 views

### 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 ...
67 views

90 views

### 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 ...
116 views

### 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 ...
18 views

### 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 ...
222 views

### 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 ...
70 views

### 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 ...
1k views

### 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 ...
87 views

### 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, ...
119 views

### 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 ...
129 views

### 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{...
260 views

### 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 ...
100 views

### 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?