Two-Phase Method for Solving LPPs Without Art. Vars.

In summary, the two phase method is not applicable in this linear programming problem since there are no artificial variables. Instead, the simplex method can be used to solve the problem by setting up an initial tableau and applying the simplex algorithm to find the optimal solution.
  • #1
Suvadip
74
0
The following LPP was asked to solve by two phase method
Max z=5x+3y
subject to
3x+5y<=15
5x+2y<=10
x,y>=0

I have applied Two phase method only in the presence of artificial variables. But in the given problem we need no artificial variable. How to proceed to solve it by two phase method?
 
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  • #2
Since there are no artificial variables in the given problem, you can solve it by the simplex method. The two phase method is used when there are artificial variables present in the linear programming problem (LPP). To solve the given LPP using the simplex method, first set up the initial tableau and then use the simplex algorithm to find the optimal solution.
 

Related to Two-Phase Method for Solving LPPs Without Art. Vars.

1. What is the Two-Phase Method for Solving LPPs Without Art. Vars.?

The Two-Phase Method is a mathematical technique used to solve Linear Programming Problems (LPPs) without the use of artificial variables. It involves breaking down a complex problem into two simpler sub-problems, and then solving them separately. The results from the sub-problems are then used to find the optimal solution for the original problem.

2. When is the Two-Phase Method typically used?

The Two-Phase Method is typically used when solving LPPs with constraints that cannot be easily converted to the standard form, which requires the use of artificial variables. It is also useful when dealing with large and complex problems, as it simplifies the solution process.

3. How does the Two-Phase Method work?

The Two-Phase Method works by first converting the LPP into a two-phase problem, where the first phase involves finding a feasible solution using artificial variables. This is followed by the second phase, where the artificial variables are removed and the original objective function is optimized to find the optimal solution.

4. What are the advantages of using the Two-Phase Method?

One of the main advantages of the Two-Phase Method is that it can solve LPPs without the need for artificial variables, which can be time-consuming and complex to deal with. It also simplifies the solution process by breaking down the problem into smaller sub-problems.

5. Are there any limitations to the Two-Phase Method?

One limitation of the Two-Phase Method is that it may not always find the optimal solution for all LPPs. It is important to carefully analyze the problem and determine if the method is suitable for solving it. Additionally, the method may not work well for problems with a large number of variables and constraints, as it can become computationally intensive.

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