1. optimal basis will not change
Consider the following problem
Max Z = 2X1 – X2 + X3
s.t.
3X1 + X2 + X3 < 60
X1 – X2 + 2X3 < 10
X1 + X X3 < 20
X1 , X2 , X3 > 0
With final tableau
If we increase b2 from 10 to 20 will the optimal basis change?
b* = S*[b + ]
All > 0,
optimal basis will not change
b. If we increase b2 from 10 to 20 what will the new objective function be?
Since b2 can go to 20, from y2=1.5, each unit increase of b2 will increase the
value of the objective function by Z = Z + 1.5*10 = 40
c. By how much can b3 change before the optimal basis will change?
b* = S*[b + ]

2. optimal basis will change
d. If we decrease b1 from 60 to 50 and increase b3 from 20 to 25,
will the optimal basis change?
b* = S*[b + ]
optimal basis will change
e. By how much can c2 vary from -1 before the basis will change?