reverse simplex method

reinout-g:

Thank you I like Serena ,

I tried what you did and this is what I got;

I had to add the extra variables u₁ and u₂ since otherwise I could not eliminate the top row (maybe there was an easier way to do that).

My slack variables saved me by directly giving me my u₁ and u₂ values.

Thanks again,
truly appreciated

Reinout

Nice!
You've completed it nice and neat!

reinout-g:

I had an exam yesterday of the class 'introduction to operations research' and one of the questions was the following;

Now I don't know whether there is anyone at this forum with knowledge of the simplex method, but I'm still wondering how this question can be done.

Hey Reinout!

First read off the optimal solution.
If you dive into your papers, you should find x1=x4=x5=0, x2=1, x3=3, Z*=c2+3c3.

Substitute back in the equations.
That should give you the value of b.

Execute the simplex method on the system with b substituted.
Use that you know that the 2nd column and the 3rd column need to be pivoted.
As a result you should get 3 equations with the unknowns c1, c2, c3, and additionally Z*=c2+3c3 that you already had.
Solving the system gives you the remaining unknowns.

Have fun!

I like Serena:

reinout-g:

I had an exam yesterday of the class 'introduction to operations research' and one of the questions was the following;

Now I don't know whether there is anyone at this forum with knowledge of the simplex method, but I'm still wondering how this question can be done.

Hey Reinout!

First read off the optimal solution.
If you dive into your papers, you should find x1=x4=x5=0, x2=1, x3=3, Z*=c2+3c3.

Substitute back in the equations.
That should give you the value of b.

Execute the simplex method on the system with b substituted.
Use that you know that the 2nd column and the 3rd column need to be pivoted.
As a result you should get 3 equations with the unknowns c1, c2, c3, and additionally Z*=c2+3c3 that you already had.
Solving the system gives you the remaining unknowns.

Have fun!

Thank you I like Serena ,

I tried what you did and this is what I got;

Knipsel22.PNG

Knipsel23.PNG

I had to add the extra variables u ₁ and u ₂ since otherwise I could not eliminate the top row (maybe there was an easier way to do that).

My slack variables saved me by directly giving me my u ₁ and u ₂ values.

Thanks again,
truly appreciated

Reinout