Please help, I have an exam in 2 hours....
And it has 1 iteration only...
I have this problem :
Maximize : $Z=2x_1+x_2$
Constraints :
$$\begin{aligned} 10x_1+10x_2&\leq 9\\ 10x_1+5x_2&\geq 1\\ x_1, x_2&\geq 0 \end{aligned}$$
With dual simplex, first of all i've changed all constraints like this and add the slack variables:
$$\begin{aligned} 10x_1+10x_2&\leq 9\\ -10x_1-5x_2&\leq -1\\ x_1, x_2, &\geq 0 \end{aligned}$$
Then
$$\begin{aligned} 10x_1+10x_2+s_1&= 9\\ -10x_1-5x_2+s_2&= -1\\ x_1, x_2, s_1, s_2 &\geq 0 \end{aligned}$$
Then, with Dual Simplex (1 iteration only), i got: $$x_1=\dfrac{1}{10}, \quad Z=\dfrac{1}{5}$$
But, when i use the Big M Method with artificial variable like this:
$$\begin{aligned} 10x_1+10x_2+s_1&=9\\ 10x_1+5x_2-s_2+R_1&=1\\ x_1, x_2,s_1,s_2,R_1&\geq 0 \end{aligned}$$
I got (using QM for Windows, there is no doubt) $$x_1=0.9, \quad Z=1.8$$
I doubt with my answer using Dual Simplex. I've tried twice and still got the same answer. Please help me. I don't care with Big M Method, i just want to know where is my mistake when i'm using Dual Simplex.
Thanks.