Find the optimal solution using dual simplex algorithm

Asked Jan 30 '19 at 21:12

Active Jan 30 '19 at 21:12

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Maximize $ z=-5x_1+10x_2+8x_3$ subject to constraints

$3x_1+5x_2+2x_3<=60$

$4x_1+4x_2+4x_3>=72$

$x_1<=0$

$x_1,x_2,x_3>=0$

Thanks for help :)

asked Jan 30 '19 at 21:12

Corn of Doom

At which step did a problem occur? One important hint: For $=$ and $\geq$ constraints you need an artificial variable each. – callculus42 Jan 30 '19 at 21:21
In the initial table on row all values are not$ <=0$ but i do not know what to do next :( – Corn of Doom Jan 30 '19 at 21:30
It´s not clear for me what do you mean by your comment. Please rephrase it. Something what is obvious is that $x_1=0$ if you combine the constraints $x_1\leq 0$ and $x_1\geq 0$. Therefore you can drop the terms with $x_1$ at the objetive function and the constraints. – callculus42 Jan 30 '19 at 21:35
The best you can do is to show your initial table. – callculus42 Jan 30 '19 at 21:39
One second pls :) – Corn of Doom Jan 30 '19 at 21:43
Here is the $\LaTeX$-code for a table: $$\begin{matrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{matrix}$$
gives

$$\begin{matrix}1 & x & x^2 \ 1 & y & y^2 \ 1 & z & z^2 \ \end{matrix}$$ You can copy the code and adjust it.
– callculus42 Jan 30 '19 at 21:44
https://pasteboard.co/HYTIwMK.png – Corn of Doom Jan 30 '19 at 21:48
Shouldn't these 2 values be smaller or equal to 0 at the beginning ? – Corn of Doom Jan 30 '19 at 21:50
all online calculators say that there is no solution but my teacher insists this can be solved using this method – Corn of Doom Jan 30 '19 at 21:51
I´ve looked at your upload. You cannot just multiply the second constraint by (-1) to get an $\leq$-constraint. You have to introduce an artificial variable like $4x_1+4x_2+4x_3-s_2+a_2=72$. – callculus42 Jan 30 '19 at 21:52
So now i have no idea what to do next. During lessons our teacher was just multiplying by -1 – Corn of Doom Jan 30 '19 at 21:57
It seems that the dual simplex algorithm is not the equivalent to the 2-Phase Simlex algorithm. Here is an equivalent question with an answer. – callculus42 Jan 30 '19 at 22:04
Yes, i saw it but is it possible to solve this problem without using big M method? – Corn of Doom Jan 30 '19 at 22:18
@callculus I saw it but i don't know how to use big M method in my case – Corn of Doom Jan 30 '19 at 22:30

Find the optimal solution using dual simplex algorithm

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