# Thread: Linear programming problem using a tabelau

1. ## Linear programming problem using a tabelau

For this linear optimization problem, we are supposed to convert the problem into canonical form and then set up a tabelau and solve using the simplex method. I am able to set it up in the tabelau but then through my calculations i am getting no where (i.e. I end up with a negative number on the far right hand side or two negatives) I'm not sure if this is supposed/easier on the computer but I just can't seem to get these numbers right. If someone can show the process or (since it is a lot of work) the final product and how many iterations it took to get there so i can attempt to get there as well. Thanks

Maximize z=-x1+3x2+x3
subject to:
-x1+2x2-7x3<=6
x1+x2-3x3<=15
x1,x2,x3>=0

2. Originally Posted by tn11631
For this linear optimization problem, we are supposed to convert the problem into canonical form and then set up a tabelau tableau (spelling!) and solve using the simplex method. I am able to set it up in the tabelau but then through my calculations i am getting no where (i.e. I end up with a negative number on the far right hand side or two negatives) I'm not sure if this is supposed/easier on the computer but I just can't seem to get these numbers right. If someone can show the process or (since it is a lot of work) the final product and how many iterations it took to get there so i can attempt to get there as well. Thanks

Maximize $z=-x_1+3x_2+x_3$ subject to:

$-x_1+2x_2-7x_3\leqslant 6$

$x_1+x_2-3x_3\leqslant 15$

$x_1,\ x_2,\ x_3\geqslant 0$
The reason that you are having trouble finding a solution is that there isn't one. In fact, you can make z arbitrarily large, for example by taking $x_1=x_2=0$ and $x_3 = \text{huge}$.

In situations like that, the simplex method breaks down and fails to come up with a solution, as you have discovered.