Consider the 2022/00 following Maximize z =3x₁ + 5x₂ Subject to X1 ≤4 2x₂ ≤ 12 3x₁ + 2x₂ ≤ 18, where x₁, x2, ≥ 0, and its associated optimal tableau is (with S₁, S2, S3 are the slack variables corresponding to the constraints 1, 2 and 3 respectively):
Basic Z X1 X2 S1 $2 S3 Solution Variables z-row 1 0 0 0 3/6 1 36
S₁ 0 0 1 1/3 -1/3 2
x2 0 0 1 0 1/2 0 6
X1 0 1 0 0 -1/3 1/3 2
Using the post-optimal analysis discuss the effect on the optimal solution of the above LP for each of the following changes. Further, only determine the action needed (write the action required) to obtain the new optimal solution for each of the cases when the following modifications are proposed in the above LP
(a) Change the R.H.S vector b=(4, 12, 18) to b'= (1,5, 34) T.|
(b) Change the R.H.S vector b=(4, 12, 18) to b'= (15,4,5) 7. [12M] LP 0 0 0 3/2