Minimize Z = 5X₁ + 4X₂

subject to

X₁ + X₂>= 60

X₁ >= 30

X₂<=40

X₁, X₂>= 0

Solve the above problem with the simplex method. Provide the value of the basic variables (BV) at tableau #3 and the optimal solution of the LP.

Notes:

• Set M = 100.
• Tableau #1 is the initial tableau where an inconsistency exists on row z.
• Tableau #2 is the tableau where the inconsistency on row z is fixed.
• Set s3 as the slack variable for constraint 3.

Select one:

BV: A2=150, A1=150, x1=150 | Optimal sol: X1 = 50, X2= 20, Z = 80

BV: A1=60, A2=30, s3=40 | Optimal sol: X1 = 30, X2= 30, Z = 270

BV: A1=30, x1=30, s3=40 | Optimal sol: X1 = 30, X2= 30, Z = 270

None of the options provided

BV: s1=2000, A1= 300, A2=100 | Optimal sol: X1 = 50, X2= 20, Z = 80