Question

Consider the following linear programming problem: Maximize 40 X1 + 30 X2 + 60X3 Subject to: X1 + X2 + X3 ≥ 90 12 X1 + 8 X2 + 10 X3 ≤ 1500 X1 = 20 X3 ≤ 100 X1 , X2 , X3 ≥ 0 How many slack, surplus, and artificial variables would be necessary if the simplex algorithm were used to solve this problem?

Answer 1

If you have a ≤-constraint, then you have to add a slack variable for each constraint.

If you have a =-constraint, then you do not have to add a slack variable for each constraint. But you have to add an artificial variable for each constraint.

If you have a ≥-constraint, then you have to substract a slack variable for each constraint. Additionally you have to add an artificial variable for each constraint.

Ans :

Number of slack = 2

Number of surplus = 1

Number of artificial = 1+1 = 2