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 + X2 - 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 1.5 Z = Z + 1.5*10 = 40 c. By how much can b3 change before the optimal basis will change? b* = S*[b + ]

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?