A question about solving a linear program using the Tableau Method

In summary, the conversation discusses solving a linear program using the tableau method. The objective is to maximize Z with constraints on X1, X2, S1, S2, and S3. The feasible region is a triangle with an origin not contained within it. The first tableau is being set up using a feasible extreme point, but there are issues completing it. The conversation also mentions changing coordinates to make the origin a vertex of the feasible set.
  • #1
Hells_Kitchen
62
0
I am trying to solve the following linear program using the tableau method:

Max Z = 25X1 + 100X2 subject to:
0.10X1 – 0.90X2 + S1 = -10
0.85X1 – 0.15X2 + S2 = -15
0.60X1 + 0.60X2 + S3 = 40
X1 , X2 , S1 , S2 , S3 ≥ 0

The feasible region is just a triangle but the origin is not contained in it.

I would like to set up the first tableau but I have to start from a feasible extreme point.

I have picked Point (50,16.67) which corresponds to S3=S1=0, but I cannot complete the whole tableau:

Basis--Z--X1--X2--S1--S2--S3---Value----Ratio

Z-----1---0---0----?---0---?-----2917
X1----0---1---0----?---0---?-----50
X2----0---0---1----?---0---?-----16.67
S2----0---0---0----?---1---?----- -25


Does anybody have any clues? Thanks.
 
Last edited:
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  • #2
I'm not really fit in the Simplex algorithm, but you could change coordinates such that the origin is a vortex of the feasible set.
 

1. What is the Tableau Method?

The Tableau Method is a mathematical technique used to solve linear programming problems. It involves creating a table, or tableau, to organize and manipulate data in order to find the optimal solution to the problem.

2. How does the Tableau Method work?

The Tableau Method works by systematically adjusting the values in the tableau until an optimal solution is found. This is done by identifying and selecting certain variables to be increased or decreased in order to improve the objective function, while also satisfying all constraints.

3. What are the advantages of using the Tableau Method?

One advantage of using the Tableau Method is that it is a relatively straightforward and systematic approach to solving linear programming problems. It also allows for quick and easy visualization of the problem and potential solutions.

4. What are the limitations of the Tableau Method?

One limitation of the Tableau Method is that it can only be used to solve linear programming problems. It also requires the problem to be in standard form, with all constraints written as equations and the objective function in terms of linear equations.

5. How do I know if the solution found using the Tableau Method is the optimal solution?

The optimal solution using the Tableau Method is found when all variables in the tableau have non-negative values and the objective function value cannot be increased any further. This means that the constraints are satisfied and the objective function is at its maximum or minimum value, depending on the problem.

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