# 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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### Simplex algorithm/basic artificial variable

How do we continue in the simplex algorithm if some artificial variable is basic ? Do we still forget about this basic artificial variable in the second phase of the simplex algorithm as we do forget ...
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### The simplex algorithm--example

Here on the page 30, why $(z_3,z_3)=1$: as written on that page 30: minimize the sum of the artificial variables, starting from the BFS where the absolute value of the artificial variable for each ...
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### Simplex Algorithm, determining Two Phase is required and choice of artificial variables

Given the following system : \begin{align*} \text{minimise } z = &2x_1 &+ 3x_2 &+ 3x_3 &+ x_4 &- 2x_5& \\ \end{align*} Subject to \begin{align*} &...
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### Simplex Algorithm: Why does Phase I deliver a BFS immediately?

When trying to solve a Linear Program (I call it primary problem below) of the form min $c^{T}x$ s.t.  $Ax = b, x \geq 0, b \geq 0$ The two phase simplex algorithm suggests to starts with the ...
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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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### Nocedal & Wright, example problem 13.1

I'm having a trouble understanding example problem 13.1 on page 371 of the 2nd edition of Nocedal & Wright: \begin{aligned} \min_x -4x_1 - 2x_2 \text{ s.t } \\ x_1 + x_2 + x_3 = 5 ...
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### Show that it has 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 has no feasible solution using SIMPLEX METHOD. It seems very logical that ...
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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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### 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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### Simplex: duplicate constraints

I'm trying to understand how the two-phase simplex algorithm works, this site explains it using a simple example: http://optlab.mcmaster.ca/feng/4O03/Two.Phase.Simplex.pdf I've tried to come up with ...
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### Duality Theorem - Optimal solution of both Primal and Dual

The Duality Theorem, in short, states that the optimal value of the Primal (P) and Dual (D) Linear Programs are the same if the solution, of either, is a basic feasible solution. My question is that ...
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### Two- phase simplex method problem

I have this problem: Minimize: $x_1+3x_2-x_3$ Subject to: \begin{align} 2x_1+x_2+3x_3 \geq 3\\ -x_1+x_2\geq1\\ -x_1-5x_2+x_3\leq4\\ x_1,x_2,x_3, \geq 0\\ \end{align} I need help solving it ...
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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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