# 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
$\frac{1}{2}{x}_{1}+\frac{1}{4}{x}_{2}\le 6$
${x}_{3}+{x}_{2}\ge 2$
${x}_{1}+{x}_{2}=10$
${x}_{1}\ge 0,{x}_{2}\ge 0$
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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blackcat1314xb
The system of linear equations in the question can't help finding a basic feasible solution since artificial variables${x}_{5},{x}_{6}\ge 0$ 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.