Solve Problem w/ Two Phase Method: Max Z

In summary, the Two Phase Method is a problem-solving technique used in linear programming to solve problems with multiple constraints and variables. It involves breaking down the problem into two phases: the first phase is used to find an initial feasible solution, and the second phase is used to optimize the solution. It is typically used when a linear programming problem has constraints that cannot be easily satisfied or when there are multiple optimal solutions. Its objective is to find the optimal solution that maximizes the objective function while satisfying all the constraints of the problem. The method involves converting the problem into standard form, finding a starting basic feasible solution, optimizing the solution, and obtaining the optimal solution. The advantages of using the Two Phase Method include its ability to handle many constraints and variables
  • #1
peteryellow
47
0
CAn somebody please help me that how can I solve the following problem with two phase method

maximize z = x_1 - 9x_2
subject to
x_1 +3x_2 +2x_3 =< 12
2x_1 + 2x_3 = 14
5x_1 +3x_2 +8x_3 = 50
x_1 >= 0, x_2>= 0, x_3>= 0.
 
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  • #2
That's a "linear programming" problem, right?

Max or min of a linear function, over a convex polygon, will occur at a vertex. Here, however, two of the "inequalities" are actually equations.

Find the point at which the planes x_1+ 3x_2+ 2x_3= 12, 2x_1+ 2x_3= 14, and 5x_1+ 3x_2+ 8x_3= 50 intersect.
 
  • #3
yes but I have to solve it by using two phase method
 

What is the Two Phase Method?

The Two Phase Method is a problem-solving technique used in linear programming to solve problems with multiple constraints and variables. It involves breaking down the problem into two phases: the first phase is used to find an initial feasible solution, and the second phase is used to optimize the solution.

When is the Two Phase Method used?

The Two Phase Method is used when a linear programming problem has constraints that cannot be easily satisfied or when there are multiple optimal solutions. It is also used when the problem has a mix of equality and inequality constraints.

What is the objective of the Two Phase Method?

The objective of the Two Phase Method is to find the optimal solution that maximizes the objective function while satisfying all the constraints of the problem. The first phase of the method aims to find an initial feasible solution, and the second phase aims to improve and optimize that solution.

What are the steps involved in the Two Phase Method?

The first step is to convert the problem into standard form by adding slack or surplus variables. Then, in the first phase, a starting basic feasible solution is found using the simplex method. In the second phase, the simplex method is used to optimize the solution found in the first phase. Finally, the optimal solution is obtained.

What are the advantages of using the Two Phase Method?

The Two Phase Method is useful for solving linear programming problems with many constraints and variables. It also allows for the handling of both equality and inequality constraints in a problem. Additionally, it guarantees an optimal solution, even if the problem has multiple optimal solutions.

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