Answer to Question #263999 in Operations Research for ddr

Question

Solve by simplex method. Max z = 2x1 -x2 +2x3, 2x1 +x2 < 10, x1 +2x2 -2x3 <20x1 +2x3 < 5, x1, x2, x3 > 0

Answer 1

After introducing slack variables

Max Z=2x₁-x₂+2x₃+0S₁+0S₂+0S₃

subject to

2x₁+x₂+S₁=10x₁+2x₂-2x₃+S₂=20x₁+2x₃+S₃=5

and x₁,x₂,x₃,S₁,S₂,S₃≥0

after iteration 1:

Negative minimum Z_j-C_j is -2 and its column index is 1. So, the entering variable is x₁.

Minimum ratio is 5 and its row index is 3. So, the leaving basis variable is S₃.

∴ The pivot element is 1.

Entering =x₁, Departing =S₃, Key Element =1

after iteration 2:

Since all Z_j-C_j≥0

Hence, optimal solution is arrived with value of variables as :

x₁=5,x₂=0,x₃=0

Max Z=10