# Solve this linear program using 2 phase simplex

Minimize $2x_1 + 3x_2 + 3x_3 + x_4 − 2x_5$

Subject to

$x_1 + 3x_2 + 4x_4 −x_5 = 2$

$x_1 + 2x_2 − 3x_4 +x_5 = 2$

$−x_1 − 4x_2 +3x_3 = 1$

$x_1, x_2, x_3, x_4, x_5 \geq 0$

Im not sure if im doing the pivoting wrong but i cant even get to the second phase without getting an infeasible solution

The minimum is given by $-\frac{15}{4}$ and will be obtained for $x_1=x_2=0,x_3=1/3,x_4=5/4,x_5=3$