Question

Given the LPP:

Max z=-2x1+x2-x3

St: x1+x2+x3<=6

  -x1+2x2<=4

  x1,x2<=0

What is the new optimal, if any, when the

a) RHS is replaced by [3  4]

b) Column a2 is changed from[1  2] to [2  5]

c) Column a1 is changed from[1  -1] to [0  -1]

d) First constraint is changed to x2-x3<=6 ?

e) New activity x6>=0 having c6=1 and a6=[-1  2] is introduced ?

Answer 1

Given primal problem is :

Maximize z = -2x₁+x₂-x₃

St: x₁+x₂+x₃ $\leq$ 6

-x₁+2x₂ $\leq$ 4

x₁,x₂ $\geq$ 0

a) After replacing RHS by [3 4], the new primal problem is :

Maximize z = -2x₁+x₂-x₃

St: x₁+x₂+x₃ $\leq$ 3

-x₁+2x₂ $\leq$ 4

x₁,x₂ $\geq$ 0

b) After changing column a₂ from [1 2] to [2 5], the new primal problem is :

Maximize z = -2x₁+x₂-x₃

St: x₁+2x₂+x₃ $\leq$ 3

-x₁+5x₂ $\leq$ 4

x₁,x₂ $\geq$ 0

c) After changing column a₁ from [1 -1] to [0 -1], the new primal problem is :

Maximize z = -2x₁+x₂-x₃

St: x₂+x₃ $\leq$ 3

-x₁+2x₂ $\leq$ 4

x₁,x₂ $\geq$ 0

e) After introducing new activity x₆ $\geq$ 0 having c₆=1 and a₆=[-1  2], the new primal problem is :

Maximize z = -2x₁+x₂-x₃+x₆

St: x₁+x₂+x₃-x₆ $\leq$ 3

-x₁+2x₂+2x₆ $\leq$ 4

x₁,x₂,x₆ $\geq$ 0