Question

Determine the optimal solution for the following linear programming problem using the Two-Phase Method. Minimize Z=4x₁​+x₂ ​ subject to 3x₁​+x₂​=3 4x₁​+3x₂​≥6 x₁​+2x₂​≤3 x₁​,x2₂≥0​

Answer 1

The Two-Phase Method is used to solve linear programming problems when the given problem has artificial variables.

Step-by-step explanation:

The Two-Phase Method is used to solve linear programming problems when the given problem has artificial variables.

In this case, we need to minimize the objective function
`Z=4x₁​+x₂` subject to certain constraints:

1. 3x₁​+x₂​=3
2. 4x₁​+3x₂​≥6
3. x₁​+2x₂​≤3
4. x₁​,x₂≥0​

Here are the steps to solve this problem using the Two-Phase Method:

1. Phase I: Add artificial variables to convert the given problem into a standard maximization problem. Solve this problem using the Simplex Method.
2. Phase II: Remove the artificial variables and solve the problem using the Simplex Method.
3. The optimal solution will be obtained at the intersection of the feasible region and the objective function.