Introducing surplus and artificial variables into the constraints:
$3X_1 - X_2 - X_3 ≥ 3 → 3X_1 - X_2 - X_3– S_1 + A_1 = 3 \\
X_1 - X_2 + X_3 ≥ 2 → X_1 - X_2 + X_3– S_2 + A_2 = 2$
Converting the minimization function to a maximization function by multiplying by ‘-1’:
Maximization $Z = -7.5X_1 + 3X_2 + 0X_3$
PHASE 1:
Maximization function becomes: $Z = 0X_1 + 0X_2 + 0S_1 + 0S_1 – A_1– A_2$
Iteration ends here, since all Cj–Zj are less than or equal to zero.
PHASE 2:
Iteration ends here.
$Max Z = -\dfrac32 ; reconverting back, Min. Z = \dfrac32 , X_1 = \dfrac15$