The following optimal Simplex table is given for a linear pr

The following optimal Simplex table is given for a linear programming problem where the decision variables are x₁ , x₂ , x₃ and the slack variables are denoted by x₄ ,…:

max x =7-66 x₁ -48 x₃ -7 x5

subject to

x₄ =3+2 x₁ +3 x₃ +1 x₅

x₂ =1-10 x₁ -8 x₃ -1 x₅

and x₁ , x₂ , x₃ 0.

Now let us assume we need to add the following constraint to the problem:

8 x₁ +7 x₂ +8 x₃ 6

Now answer the following:

(a) Add this new constraint to the current Simplex table, is this table optimal? (answer: 0 for no, 1 for yes)

(b) What is the optimal solution for this modified problem =

(c) If the table is non-optimal, which variable should leave the basis? (answer: 0 for none, else the index of the variable)

(d) Assume we decide to add a very large number of constraints to the problem should we solve the dual problem (answer: 0) or the primal problem (answer: 1) ?

Solution

8 x1 +7 x2 +8 x3 6

now add a slack variable to this

8x1 + 7x2 + 8x3 +s1 =6 s1>=0