Consider the following LP problem: Maximize Z = 2 x 1 - x 2 + x 3 s.t. 3 x 1 - 2
ID: 3027912 • Letter: C
Question
Consider the following LP problem:
Maximize Z = 2x1 - x2 + x3
s.t. 3x1 - 2x2 + 2x3 15
-x1 + x2 + x3 3
x1 - x2 + x3 4
xi 0, i = 1,2,3.
If we let x4 , x5 , and x6 to be the slack variables for the respective constraints, the simplex method yields the following final set of equations:
1. Conduct sensitivity analysis for the RHS, i.e., provide ranges for each bi , i = 1,2,3, in which the current solution remains optimal.
2. Find the solution for the problem if the RHS changes to:
b = ( 10
4
2)
(one column matrix)
(0) Z +2x3 +x4 +xs =18 x2 + 5x3 +x4 + 3x5 =24 2x3 +x5 +x6= 7 (3) x1+4x3 +x4 + 2x5 =21. 18 5.5 ss 4.4 xx 3.3 0123Explanation / Answer
1. solve by Simplex method
represent by tabular form:
Table 1
--------------------------------------------------------------
x1 x2 x3 s1 s2 s3 z
-------------------------------------------------------------
3 -2 2 1 0 0 0 15
-1 1 1 0 1 0 0 3
1 -1 1 0 0 1 0 4
-2 1 -1 0 0 0 1 0
Table 2
--------------------------------------------------------------
x1 x2 x3 s1 s2 s3 z
-------------------------------------------------------------
0 1 -1 1 0 -3 0 3
0 0 2 0 1 1 0 7
1 -1 1 0 0 1 0 4
0 -1 1 0 0 2 1 8
Table 3
--------------------------------------------------------------
x1 x2 x3 s1 s2 s3 z
-------------------------------------------------------------
0 1 -1 1 0 -3 0 3
0 0 2 0 1 1 0 7
1 0 0 1 0 -2 0 7
0 0 0 1 0 -1 1 11
Table 4
--------------------------------------------------------------
x1 x2 x3 s1 s2 s3 z
-------------------------------------------------------------
0 1 5 1 3 0 0 24
0 0 2 0 1 1 0 7
1 0 4 1 2 0 0 21
0 0 2 1 1 0 1 18
then the solution : z = 18; x1 = 21, x2 = 24, x3 = 0
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