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how can we explain that the all slack point is feasible

how can we explain that the all slack point is feasible when solving a linear programming problem using the simplex method Thanks in advance, i appreciate all the help.
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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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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\\ ...
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56 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 ...
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91 views

Simplex Method with negative R.H.S

Maximize $2x_1 - 6x_2$ Subject to $-x_1 - x_2 - x_3 \leq -2 \\ 2x_1 - x_2 + x_3 \leq 1 $ I create an auxiliary problem: Maximize $-x_0$ Subject to $-x_1 - x_2 - x_3 -x_0 \leq -2 \\ 2x_1 - x_2 ...
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60 views

Represent if-else or OR condition in a linear equation (optimisation with simplex algorithm)

I would like to write some linear equations and inequations to state that the sum of all possive x - C is smaller than L. As my ...
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1answer
68 views

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 [2] as 0.5/0.5=1 instead. Could ...
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36 views

sensitivity analysis - help!

Hi guys I am doing a quesetion on simplex method and am stuck on the second part of the sensitbity analysis question: I am stuck on the part that is asking for 12 + n. I know that I am changing ...
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152 views

Casio fx-83gt - help! Linear Programming

Hi guys I'm studying a module called Operational Research and in particular linear programming. I am doing the simplex method and as anyone who studies linear programming would know, you need to ...
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2answers
100 views

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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42 views

On the injection of exactly two artificial variables into the Phase I of a two-phase simplex

I am relatively new still to linear optimization and as I understand it, the two phase method is a common practice for finding the bfs before using the simplex or a simplex like solver (a solver ...
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88 views

Simplex method Dual phase precision problem

I am trying to implement simplex method algorithm in PHP language. But I am facing with precision problem. For example if I try to solve these equations: ...
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172 views

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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226 views

linear program-Simplex method-Dual problem

At an exercise I am asked to solve a linear program using the simplex method(in Matlab).Then I have to formulate the dual of this problem and read off an optimal solution of the dual problem from the ...
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53 views

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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1answer
18 views

Are these constraints correct?

A bike dealer buys at a wholesale: bikes, scooters and child's saddles. He wants maximum profit. He buys the bike (x) for 300, the scooter (y) for 1200 and the saddle (z) for 36. A bike takes ...
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1answer
681 views

Reduced cost in the Phase II of the two-phase Simplex?

My lecture slides outline how the two-phase simplex works: this table shows the end result of the phase I for the standard-form problem and the auxliary table of the phase I here. I understood until ...
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509 views

Reduced cost vector in the phase I of the Two-phase simplex?

I am trying to understand the part in red. The left is the standard form problem and the right is the auxiliary problem. Now I can understand until the red i.e. $\bar c =(-1,-1,-3,-1,-2,0,0,0)$. The ...
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1answer
176 views

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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1answer
403 views

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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2answers
353 views

Reduced cost zero for the two-phase Simplex?

I cannot understand the line -12, -4, -5, 1, 1, -1, 0, 0, 0. Now the formula $\bf c - \bf A ^t \bf y$ when $c=0$ will result into the line. It is just many times a ...