Solve the following linear program using (Two Phase) Simplex Method: Minimize 2x_1+3x_2 Subject to 1/2x_1+1/4x_2<=6, x_3+x_2>=2, x_1+x_2=10, x_1>=0,x_2>=0

Iris Vaughn 2022-10-18 Answered
Solve the following linear program using (Two Phase) Simplex Method:
Minimize 2 x 1 + 3 x 2
Subject to
1 2 x 1 + 1 4 x 2 6
x 3 + x 2 2
x 1 + x 2 = 10
x 1 0 , x 2 0
My solution:
0.5 x 1 + 0.25 x 2 + x 3 = 6
x 1 3 x 2 + x 4 = 2
x 1 + x 2 = 10
Is this correct?
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Answers (1)

blackcat1314xb
Answered 2022-10-19 Author has 19 answers
The system of linear equations in the question can't help finding a basic feasible solution since artificial variables x 5 , x 6 0 are missed in the second and third constraints.
0.5 x 1 + 0.25 x 2 + x 3 = 6
x 1 3 x 2 + x 4 + x 5 = 2
x 1 + x 2 + x 6 = 10
To find a basic feasible solution to the original LP, we use the two-phase simplex method.
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